Yes, there are parts of the universe traveling away from us at faster than the speed of light. In fact, it's quite likely that the universe is infinitely big and an infinitely large part of it is traveling away from us at faster than the speed of light.

This fact, however, does not allow information to be transmitted between two points in space at faster than the speed of light. That's the important constraint here. Causality is only violated when you transmit INFORMATION between TWO POINTS at faster than the speed of light.