Fix an integer k⩾3k⩾3. A *k*-uniform hypergraph is simple if every two edges share at most one vertex. We prove that there is a constant *c* depending only on *k* such that every simple *k*-uniform hypergraph *H* with maximum degree Δ has chromatic number satisfying

This implies a classical result of Ajtai, Komlós, Pintz, Spencer and Szemerédi and its strengthening due to Duke, Lefmann and Rödl. The result is sharp apart from the constant *c*.