But the answer is old and does not include the chat technology.
Actually it's more or less up-to-date, and does indeed include chat technology, because the chat is built on the same stack.
I am most interested in how they implemented Comet (aka HTTP push) in .NET.
We didn't originally. We went with a simple polling model; see Why is the Stack Exchange chat room using simple polling instead of other Comet techniques?. We later added (optional) support for Websockets; see Does the chat system support sending data via WebSockets?. We're using a custom-written Websocket server that Marc wrote (SignalR did not yet exist back when this was added).
We're planning on putting up a blog post at some point to give an overview of some of the ideas and decisions that went into the chat.
If you have any specific questions feel free to ask them.
Some interesting questions that already exist and that offer some insight and discussions (in no particular order):