By definition, a Type Ic supernova (SN Ic) does not have conspicuous lines of hydrogen or helium in its optical spectrum. SNe Ic usually are modelled in terms of the gravitational collapse of bare carbon-oxygen cores. We consider the possibility that the spectra of ordinary (SN 1994I-like) SNe Ic have been misinterpreted, and that SNe Ic eject hydrogen. An absorption feature usually attributed to a blend of Si II 6355 and C II 6580 may be produced by H-alpha. If SN 1994I-like SNe Ic eject hydrogen, the possibility that hypernova (SN 1998bw-like) SNe Ic, some of which are associated with gamma-ray bursts, also eject hydrogen should be considered. The implications of hydrogen for SN Ic progenitors and explosion models are briefly discussed.

Accepted by PASP. Several significant changes including one additional figure