Gamma-ray bursts (GRBs) are short, intense flashes of soft gamma-rays coming from the distant Universe. Long-duration GRBs (those lasting more than approximately 2 s) are believed to originate from the deaths of massive stars, mainly on the basis of a handful of solid associations between GRBs and supernovae. GRB 060614, one of the closest GRBs discovered, consisted of a 5-s hard spike followed by softer, brighter emission that lasted for approximately 100 s (refs 8, 9). Here we report deep optical observations of GRB 060614 showing no emerging supernova with absolute visual magnitude brighter than M(V) = -13.7. Any supernova associated with GRB 060614 was therefore at least 100 times fainter, at optical wavelengths, than the other supernovae associated with GRBs. This demonstrates that some long-lasting GRBs can either be associated with a very faint supernova or produced by different phenomena.