Mass transport along grain boundaries in alloys depends not only on the atomic structure of the boundary, but also its chemical make-up. In this work, we use molecular dynamics to examine the effect of Cr alloying on interstitial and vacancy-mediated transport at a variety of grain boundaries in Ni. We find that, in general, Cr tends to reduce the rate of mass transport, an effect which is greatest for interstitials at pure tilt boundaries. However, there are special scenarios in which it can greatly enhance atomic mobility. Cr tends to migrate faster than Ni, though again this depends on the structure of the grain boundary. Further, grain boundary mobility, which is sometimes pronounced for pure Ni grain boundaries, is eliminated on the time scales of our simulations when Cr is present. We conclude that the enhanced transport and grain boundary mobility often seen in this system in experimental studies is the result of non-equilibrium effects and is not intrinsic to the alloyed grain boundary. These results provide new insight into the role of grain boundary alloying on transport that can help in the interpretation of experimental results and the development of predictive models of materials evolution.