We present first results for masses ofspin-3/2 baryons in lattice QCD, using a novel fat-link clover fermion action in which only the irrelevant operators are constructed using fat links. In theisospin-1/2 sector; we observe, after appropriate spin and parity projection, a strong signal for theJP =3/2− state, and find good agreement between the½+ mass and earlier nucleon mass simulations with aspin-½ interpolating field. For theisospin-3/2 Δ states, clear mass splittings are observed between the various½±and3/2± channels, with the calculated level orderings in good agreement with those observed empirically.