Queue<T> is not threadsafe.
If you were using .Net 4 or later, I would recommend that you use BlockingCollection<T>.
Unfortunately, you can't use that, but there are several implementations of a Concurrent Queue kicking around.
Have a look at this one in the answer from Marc Gravel. Unfortunately that doesn't have a Peek() method.
Here's a class I used to use before .Net 4 came out; perhaps this might be of interest to you. It's not the greatest implementation; we were using it more as a placeholder until .Net 4 came out. Even so, here it is:
/// <summary>A bounded blocking queue.</summary>
/// <typeparam name="T">The element type of the queue, which must be a reference type.</typeparam>
public sealed class BoundedBlockingQueue<T>: IDisposable where T: class
{
    #region Construction and disposal
    /// <summary>Constructor.</summary>
    /// <param name="maxQueueSize">
    /// The maximum size of the queue.
    /// Calls to <see cref="Enqueue"/> when the queue is full will block until at least one item has been removed.
    /// Calls to <see cref="Dequeue"/> when the queue is empty will block until a new item is enqueued.
    /// </param>
    public BoundedBlockingQueue(int maxQueueSize)
    {
        if (maxQueueSize <= 0)
        {
            throw new ArgumentOutOfRangeException("maxQueueSize");
        }
        _queue                  = new Queue<T>(maxQueueSize);
        _itemsAvailable         = new Semaphore(0, maxQueueSize);
        _spaceAvailable         = new Semaphore(maxQueueSize, maxQueueSize);
        _queueStopped           = new ManualResetEvent(false);
        _queueStoppedAndEmpty   = new ManualResetEvent(false);
        _stoppedOrItemAvailable = new WaitHandle[] { _queueStopped, _itemsAvailable };
    }
    /// <summary>Disposal.</summary>
    public void Dispose()
    {
        if (_itemsAvailable != null)
        {
            _itemsAvailable.Close();
            _spaceAvailable.Close();
            _queueStopped.Close();
            _queueStoppedAndEmpty.Close();
            _itemsAvailable = null;          // Use _itemsAvailable as a flag to indicate that Dispose() has been called.
        }
    }
    #endregion Construction and disposal
    #region Public properties
    /// <summary>The number of items currently in the queue.</summary>
    public int Count
    {
        get
        {
            throwIfDisposed();
            lock (_queue)
            {
                return _queue.Count;
            }
        }
    }
    /// <summary>Has <see cref="Stop"/> been called?</summary>
    public bool Stopped
    {
        get
        {
            throwIfDisposed();
            return _stopped;
        }
    }
    #endregion Public properties
    #region Public methods
    /// <summary>
    /// Signals that new items will no longer be placed into the queue.
    /// After this is called, calls to <see cref="Dequeue"/> will return null immediately if the queue is empty.
    /// Before this is called, calls to <see cref="Dequeue"/> will block if the queue is empty.
    /// Attempting to enqueue items after this has been called will cause an exception to be thrown.
    /// </summary>
    /// <remarks>
    /// If you use a different thread to enqueue items than the thread that calls Stop() you might get a race condition.
    /// 
    /// If the queue is full and a thread calls Enqueue(), that thread will block until space becomes available in the queue.
    /// If a different thread then calls Stop() while the other thread is blocked in Enqueue(), the item enqueued by the other
    /// thread may become lost since it will be enqueued after the special null value used to indiciate the end of the
    /// stream is enqueued.
    /// 
    /// To prevent this from happening, you must enqueue from the same thread that calls Stop(), or provide another
    /// synchronisation mechanism to avoid this race condition.
    /// </remarks>
    public void Stop()
    {
        throwIfDisposed();
        lock (_queue)
        {
            _queueStopped.Set();
            _stopped = true;
        }
    }
    /// <summary>
    /// Returns the front item of the queue without removing it, or null if the queue is currently empty.
    /// A null return does NOT indicate that <see cref="Stop"/> has been called.
    /// This never blocks.
    /// </summary>
    /// <returns>The front item of the queue, or null if the queue is empty.</returns>
    public T Peek()
    {
        throwIfDisposed();
        T result;
        lock (_queue)
        {
            if (_queue.Count > 0)
            {
                result = _queue.Peek();
            }
            else
            {
                result = null;
            }
        }
        return result;
    }
    /// <summary>
    /// Enqueues a new non-null item.
    /// If there is no room in the queue, this will block until there is room.
    /// An exception will be thrown if <see cref="Stop"/> has been called.
    /// </summary>
    /// <param name="item">The item to be enqueued. This may not be null.</param>
    public void Enqueue(T item)
    {
        throwIfDisposed();
        if (item == null)
        {
            throw new ArgumentNullException("item");
        }
        if (_stopped)
        {
            throw new InvalidOperationException("Attempting to enqueue an item to a stopped queue.");
        }
        this.enqueue(item);
    }
    /// <summary>
    /// Dequeues the next available item.
    /// If <see cref="Stop"/> has been called, this returns null if the queue is empty.
    /// Otherwise it blocks until an item becomes available (or <see cref="Stop"/> is called).
    /// </summary>
    /// <returns>The next available item, or null if the queue is empty and stopped.</returns>
    public T Dequeue()
    {
        throwIfDisposed();
        if (_isQueueStoppedAndEmpty)
        {
            return null;
        }
        WaitHandle.WaitAny(_stoppedOrItemAvailable);
        lock (_queue)
        {
            if (_stopped && (_queue.Count == 0))
            {
                _isQueueStoppedAndEmpty = true;
                _queueStoppedAndEmpty.Set();
                return null;
            }
            else
            {
                T item = _queue.Dequeue();
                _spaceAvailable.Release();
                return item;
            }
        }
    }
    /// <summary>Waits forever for the queue to become empty AND stopped.</summary>
    public void WaitUntilStoppedAndEmpty()
    {
        throwIfDisposed();
        WaitUntilStoppedAndEmpty(Timeout.Infinite);
    }
    /// <summary>Waits up to the specified time for the queue to become empty AND stopped.</summary>
    /// <param name="timeoutMilliseconds">The maximum wait time, in milliseconds.</param>
    /// <returns>True if the wait succeeded, false if it timed-out.</returns>
    public bool WaitUntilStoppedAndEmpty(int timeoutMilliseconds)
    {
        throwIfDisposed();
        return _queueStoppedAndEmpty.WaitOne(timeoutMilliseconds);
    }
    #endregion Public methods
    #region Private methods
    /// <summary>Enqueues a new item (which may be null to indicate the last item to go into the queue).</summary>
    /// <param name="item">An item to enqueue.</param>
    private void enqueue(T item)
    {
        _spaceAvailable.WaitOne();
        lock (_queue)
        {
            _queue.Enqueue(item);
        }
        _itemsAvailable.Release();
    }
    /// <summary>Throws if this object has been disposed.</summary>
    private void throwIfDisposed()
    {
        if (_itemsAvailable == null)
        {
            throw new ObjectDisposedException(this.GetType().FullName);
        }
    }
    #endregion Private methods
    #region Fields
    /// <summary>
    /// Contains wait handles for "stopped" and "item available".
    /// Therefore using this for WaitAny() will wait until the queue is stopped
    /// or an item becomes available, whichever is the sooner.
    /// </summary>
    private readonly WaitHandle[] _stoppedOrItemAvailable;
    private Semaphore _itemsAvailable;
    private volatile bool _stopped;
    private volatile bool _isQueueStoppedAndEmpty;
    private readonly Queue<T> _queue;
    private readonly Semaphore _spaceAvailable;
    private readonly ManualResetEvent _queueStopped;
    private readonly ManualResetEvent _queueStoppedAndEmpty;
    #endregion Fields
}
And here's an old unit test for it. It's not a very good unit test; it tests too many things at once and has some other problems, but it will demonstrate how to use the queue:
[TestMethod]
public void TestBoundedBlockingQueue()
{
    int maxQueueSize = 8;
    using (var queue = new BoundedBlockingQueue<string>(maxQueueSize))
    {
        // Fill the queue, but don't block.
        for (int i = 0; i < maxQueueSize; ++i)
        {
            int start1 = DateTimeFunctions.TickCount;
            queue.Enqueue(i.ToString());
            int elapsed1 = DateTimeFunctions.TickCount - start1;
            Assert.IsTrue(elapsed1 < 100, "Took too long to enqueue an item.");  // Shouldn't have taken more than 100 ms to enqueue the item.
        }
        // Now if we try to enqueue something we should block (since the queue should be full).
        // We can detect this by starting a thread that will dequeue something in a few seconds
        // and then seeing how long the main thread took to enqueue something.
        // It should have taken around the thread sleep time (+/- half a second or so).
        int sleepTime = 2500;
        int tolerance = 500;
        Worker.Run(()=>{Thread.Sleep(sleepTime); queue.Dequeue();}, "TestBoundedBlockingQueue Dequeue()");
        int start2 = DateTimeFunctions.TickCount;
        queue.Enqueue(maxQueueSize.ToString());
        int elapsed2 = DateTimeFunctions.TickCount - start2;
        Assert.IsTrue(Math.Abs(elapsed2 - sleepTime) <= tolerance, "Didn't take the right time to enqueue an item.");
        // Now verify that the remaining items in the queue are the expected ones,
        // i.e. from "1".."maxQueueSize" (since the first item, "0", has been dequeued).
        for (int i = 1; i <= maxQueueSize; ++i)
        {
            Assert.AreEqual(i.ToString(), queue.Dequeue(), "Incorrect item dequeued.");
        }
        Assert.AreEqual(0, queue.Count);
        // Now if we try to dequeue something we should block (since the queue is empty).
        // We can detect this by starting a thread that will enqueue something in 5 seconds
        // and then seeing how long the main thread took to dequeue something.
        // It should have taken around 5 seconds (+/- half a second or so).
        string testValue = "TEST";
        Worker.Run(()=>{Thread.Sleep(sleepTime); queue.Enqueue(testValue);}, "TestBoundedBlockingQueue Enqueue()");
        start2 = DateTimeFunctions.TickCount;
        Assert.AreEqual(testValue, queue.Dequeue(), "Incorrect item dequeued");
        elapsed2 = DateTimeFunctions.TickCount - start2;
        Assert.IsTrue(Math.Abs(elapsed2 - sleepTime) <= tolerance, "Didn't take the right time to enqueue an item.");
    }
}