Is it a good 300 W PSU? Or a Chinese no name? If it's a brand name you can do 7770, or 7750 if you only have a single slot available.
I have a shuttle PC that is running a Bronze 300 W PSU and I'm running an Ivy Pridge i5 and a Radeon 7770 no problem.
270W is the max pull for the entire PC during high load and gaming.