What power supply do you have? The 6870 uses considerably more power than a 3400. But that being said if your PSU meets the specifications listed on the XFX site it should be fine.
the required specifications were
External Power - 6-Pins: 2
Minimum Power Supply Requirement:500 Watt
* There will be an amps on the 12V rail requirement that you should look up in the manual before buying