In quantum field theory, the entropy of a region is nonzero, even in the vacuum state, due to entanglement between the fields inside and outside the region. But in field theories with gravitational anomalies, the entropy of a region is no longer invariant under a Lorentz boost near the boundary. Thus there is an anomaly in the entanglement entropy, even on backgrounds on which the gravitational anomaly vanishes. I will show how this effect can be derived by physical arguments based on the propagation of chiral modes, and from the path integral, in various dimensions. Based on arXiv:1509.04325.