We prove that the strong chromatic index of a 2-degenerate graph is linear in the maximum degree Δ. This includes the class of all chordless graphs (graphs in which every cycle is induced) which in turn includes graphs where the cycle lengths are multiples of four, and settles a problem by Faudree et al. (Ars Combin 29(B) (1990), 205-211). © 2012 Wiley Periodicals, Inc.