Is it possible to create a class in .NET 4 with:
- an indexer,
 - a property named "Item"?
 
For example, this C# class will not compile for me:
public class MyClass
{
    public object Item { get; set; }
    public object this[string index] { get { return null; } set { } }
}
The compiler gives an error CS0102:
The type 'MyClass' already contains a definition for 'Item'
although I am only explicitly defining Item once.