Over the past decade, our physical understanding of gamma-ray bursts (GRBs) has progressed rapidly, thanks to the discovery and observation of their long-lived afterglow emission. Long-duration (> 2 s) GRBs are associated with the explosive deaths of massive stars ('collapsars', ref. 1), which produce accompanying supernovae; the short-duration (< or = 2 s) GRBs have a different origin, which has been argued to be the merger of two compact objects. Here we report optical observations of GRB 060614 (duration approximately 100 s, ref. 10) that rule out the presence of an associated supernova. This would seem to require a new explosive process: either a massive collapsar that powers a GRB without any associated supernova, or a new type of 'engine', as long-lived as the collapsar but without a massive star. We also show that the properties of the host galaxy (redshift z = 0.125) distinguish it from other long-duration GRB hosts and suggest that an entirely new type of GRB progenitor may be required.