not really recommended. even if it is a high quality PSU and the rest of your system isnt energy intensive, you would be putting too much pressure on your psu, assuming it works at load at all.
Is it possible to run a 5770 on a 300 PSU?
I have seen it happen but could it mess up if i am not careful?
I'd rather be on the safe side and buy a 400 W PSU. Also, what's the brand and model name for that PSU. If it's was Antec Earthwatts 380 W, then it would run for sure. Antec makes great and solid PSUs. But if it's one of it's one of those PSUs that you get within that cabinet for the CPU, then I'd suggest yo change it before buying the card.