WebSockets is a technology designed to simplify much of the complexity around bi-directional, full-duplex communications channels, over a single Transmission Control Protocol (TCP) socket. It can be implemented in web browsers, web servers as well as used by any client or server application. The WebSockets API is currently being standardized by the W3C Web Applications Working Group and the protocol is being standardized by IETF Hypertext Bidirectional (HyBi) Working Group.
Below is an example from http://html5labs.com/ (sorry for the iframe 
)
HTML5Labs is where Microsoft prototypes early and unstable specifications from web standards bodies such as W3C. Sharing these prototypes helps us have informed discussions with developer communities, and enables us to provide better feedback on draft specifications based on this implementation experience. To find out more about HTML5Labs, read the blog by Dean Hachamovitch, Corporate Vice President for Internet Explorer, and the blog by Jean Paoli, General Manager for Interoperability Strategy.
If you want to run your own chat app like above (and save yourself a lot of troubleshooting), I suggest you check this blog post on how to install the WebSockets prototype.
Here’s an example of me talking to myself (that happens quite a lot in real life actually)
Follow