Battlefield 3 is currently only available digitally through EA's Origin service, but two small bits of evidence may indicate DICE's shooter will be making an appearance on Valve's rival Steam service at some point.
Exhibit A comes via a competition being held on Sapphire Select Club website, which lists one of the prizes as "[o]ne (1) PC Game code for Battlefield 3, redeemable for the game on Steam". However this may very well be an honest mistake on its part.
Exhibit B is a few lines telling code found within Battlefield 3's Punk Buster install, which mentions Steam specifically:
C:\Program Files (x86)\Electronic Arts\Battlefield 3\
C:\Program Files (x86)\Steam\SteamApps\common\battlefield 3\
C:\Program Files\Steam\SteamApps\common\battlefield 3\
C:\Program Files\Electronic Arts\Battlefield 3\
Again, this may be something that the folks over at Punk Buster just didn't bother removing, so take it all with a grain of salt.
EA has previously said the snub is due to DLC/patch restrictions on Valve's service, but offered a little hope by saying it could still "work out an agreement where Steam can carry Battlefield 3."