Well, it's not horrible. If the rest of your system does not draw too much power then it should be o.k., but personally I would recommend purchasing a quality PSU of at least 450W. Well, you can get away with a 380W Antec Earth Watts or a 400W Corsair/FSP/ or PC Power & Cooling.
I think they recommend a min of 450W or more for any GPU that requires a 6pin PCI-E power connector. the 4770 does use less power than the 4850, so you would be safer with that. If the card is underpowered, you'll probably know pretty quick because you'll probably get poor performance, artifacts and things like that if it is.