Valve have officially pushed the Counter Strike Source game onto Linux, as the CDR suggests: Steamdb.info
I had a few issues initially with being able to even get the game running, however I've included below some workarounds. The first being that the game doesn't launch from the Steam interface, it opens then immediately closes. You can get some better output and actually launch the game by running it from the root directory; which will be STEAM/steamapps/USERNAME/Counter-Strike Source/
After running the hl2.sh file provided, you may end up with this:
Setup file 'gameinfo.txt' doesn't exist in subdirectory 'hl2'.
Check your -game parameter or VCONFIG setting.
I had to edit the hl2.sh script to force it to launch the cstrike mod.
The next issue I found was that the game didn't recognise my Steam login; on looking at the logs I get this:
[S_API FAIL] SteamAPI_Init() failed; no appID found.
Either launch the game from Steam, or put the file steam_appid.txt containing the correct appID in your game folder.
Again, a simple fix, just add a steam_appid.txt file to the same directory as hl2.sh with the number "240" inside.
The last issue I've got is one without a fix right now. I can't connect to 99% of servers because I get an error with the message "You are in insecure mode. You must restart before you can connect to secure servers."
I did manage to connect to a non-VAC secured server and play a couple of *really terrible* rounds before the server shut down though.