Analyses of supernovae (SNe) have revealed two main types of progenitors: exploding white dwarfs and collapsing massive stars. Here we describe SN 2002bj, which stands out as different from any SN reported to date. Its light curve rose and declined very rapidly, yet reached a peak intrinsic brightness greater than -18 magnitude. A spectrum obtained 7 days after discovery shows the presence of helium and intermediate-mass elements, yet no clear hydrogen or iron-peak elements. The spectrum only barely resembles that of a type Ia SN, with added carbon and helium. Its properties suggest that SN 2002bj may be representative of a class of progenitors that previously has been only hypothesized: a helium detonation on a white dwarf, ejecting a small envelope of material. New surveys should find many such objects, despite their scarcity.