The 4870 is the loudest part of the system I've managed to build. (Also a Sapphire, using ATI's reference design, but with increased memory).Apart from the 4870 fan noise it would be very quiet, maybe wrong to say whisper quiet but considering the amount of fans etc that Dragonforce pointed out it's a lot better than I expected.
It's not too bad, but it's certainly not "quiet" when loaded.