Get that Linux feeling - on Windows
Are there chat channels for the project?
Yes, indeed. There are two offical IRC channels on Freenode.net.
The Freenode channel #cygwin is for user communication and user questions. This is the right channel if you want to discuss running Cygwin and problems with Cygwin setup, etc. It's not a bug report channel. For this, use the Cygwin mailing list. Help on the mailing list will also be of higher quality, usually, but for the occasional problem discussion, the #cygwin channel is pretty neat.
The Freenode channel #cygwin-developers is reserved for communication between Cygwin developers and Cygwin package maintainers. It's not a channel for reporting bugs and it's not a channel for idle "it would be nice if Cygwin ..." type of discussion. Only join this channel if you honestly, seriously want to get your hands dirty and work for the project. Otherwise, expect to be ignored.
Incidentally, Cygwin itself comes with a few IRC clients like ii, irssi, naim, tinyirc, tirc and weechat. Please see the Freenode homepage for help setting up your IRC client to connect to Freenode.