This will be possible via the navigator interface as shown below:
navigator.tcpPermission.requestPermission({remoteAddress:"127.0.0.1", remotePort:6789}).then(
  () => {
    // Permission was granted
    // Create a new TCP client socket and connect to remote host
    var mySocket = new TCPSocket("127.0.0.1", 6789);
    // Send data to server
    mySocket.writeable.write("Hello World").then(
        () => {
            // Data sent sucessfully, wait for response
            console.log("Data has been sent to server");
            mySocket.readable.getReader().read().then(
                ({ value, done }) => {
                    if (!done) {
                        // Response received, log it:
                        console.log("Data received from server:" + value);
                    }
                    // Close the TCP connection
                    mySocket.close();
                }
            );
        },
        e => console.error("Sending error: ", e)
    );
  }
);
More details are outlined in the w3.org tcp-udp-sockets documentation.
http://raw-sockets.sysapps.org/#interface-tcpsocket
https://www.w3.org/TR/tcp-udp-sockets/
Another alternative is to use Chrome Sockets
Creating connections
chrome.sockets.tcp.create({}, function(createInfo) {
  chrome.sockets.tcp.connect(createInfo.socketId,
    IP, PORT, onConnectedCallback);
});
Sending data
chrome.sockets.tcp.send(socketId, arrayBuffer, onSentCallback);
Receiving data
chrome.sockets.tcp.onReceive.addListener(function(info) {
  if (info.socketId != socketId)
    return;
  // info.data is an arrayBuffer.
});
You can use also attempt to use HTML5 Web Sockets (Although this is not direct TCP communication):
var connection = new WebSocket('ws://IPAddress:Port');
connection.onopen = function () {
  connection.send('Ping'); // Send the message 'Ping' to the server
};
http://www.html5rocks.com/en/tutorials/websockets/basics/
Your server must also be listening with a WebSocket server such as pywebsocket, alternatively you can write your own as outlined at Mozilla