An internal beta is starting next week while in October it will open up to a private external beta for about one thousand Linux users. The beta includes Steam, one Valve game (should be Left 4 Dead 2), and support for Ubuntu 12.04 and newer.
Not yet part of the beta is the Steam Big Picture mode support and additional Valve games. The timing though ended up being nearly spot on from my comments months ago about seeing a beta around the time of my annual pilgrimage, a.k.a. Oktoberfest.
The details were shared via the Valve blog.