SUPERNOVAE are classified observationally as type I (which have no hydrogen emission lines in their optical spectra) or type II (which do have hydrogen lines), and are further subdivided(1) into types Ia, Ib, Ic, IIP, IIL and IIb. Type II supernovae are generally thought to result from the explosion of massive stars, and type Ia supernovae from white-dwarf stars that have accreted sufficient mass from a companion to trigger explosion(1,2). The origins of types Ib and Ic are much less clear. The Ic class has been particularly controversial, with two main alternatives : the explosion of a massive star that has lost its hydrogen and helium envelopes through fast stellar winds, exposing the carbon- and oxygen-rich core; or the transfer of material to a companion, leaving a small, bare carbon-oxygen (C + O) star which subsequently explodes(3,4). We show here that the observed characteristics of SN1994I (in the nearby galaxy NGC5194), which has recently(5,6) been classified as type Ic, are best understood on the basis of the second of the two alternatives above : that the progenitor was in a close binary system and lost its outer envelopes, leaving a C + O star (of mass approximate to 2 solar masses) which exploded when its iron core collapsed.