FX 6300 is a nice chip and won't bottleneck that card. I do recommend running an aftermarket cooler at the very least, and bumping the multiplier of the CPU to match an FX 6350. The Athlon II will bottleneck, especially in newer titles. Its lack of an L3 cache has shown to severely hurt performance in newer titles.
The Athlon II x4 is not recomanded for such a card , the Hd 7870-XT is basically a light version of the high end : HD 7950..and as logainofhades stated : the lack of cache will hold this card down from giving the 100% performances, the FX 4300 is another AMD AM3+ quad core that could give much better performances and FX6300 is greater choise.