  Roughly a dozen X-ray binaries are presently known in which the compact
accreting primary stars are too massive to be neutron stars. These primaries
are identified as black holes, though there is as yet no definite proof that
any of the candidate black holes actually possesses an event horizon. We
discuss how Type I X-ray bursts may be used to verify the presence of the event
horizon in these objects. Type I bursts are caused by thermonuclear explosions
when gas accretes onto a compact star. The bursts are commonly seen in many
neutron star X-ray binaries, but they have never been seen in any black hole
X-ray binary. Our model calculations indicate that black hole candidates ought
to burst frequently if they have surfaces. Based on this, we argue that the
lack of bursts constitutes strong evidence for the presence of event horizons
in these objects.
