If you want to objectively, accurately and scientifically determine what PSU power is required for your Vid card and PC in both watts and 12v rail amps., the forum Utility link below will show you how easy it is to calculate this information and objectively determine which PSUs are quality built, reliable PSUs that can meet your needs. Be advised that the available 12v rail amps. is just as important as the total PSU wattage. You need both to be correct.
Logically, if your PSU can run 3870x2 just fine then you'll be okay running a single HD6850. But again, we need more info here just to be sure, tell us your FULL specs, first.
CPU? RAM? board? PSU? Monitor? Budget?