I'm running four with a Corsair 1200AX, but you could get away with less. I'd recommend the Corsair AX860i; it's 860 watts and super efficient. Mine is powering two 7950s and never draws more than 415 watts... should be plenty of headroom for three 7970s, especially if you undervolt them a bit.
Hi, about these 415 watts how did you achieve that? It seems very good, considering each 7950 as 200W. Is this from wall - do you use some kill-a-watt? Or is this number from Corsair software provided with AX860i?