  To ask a question about a black hole in quantum gravity, one must restrict
initial or boundary data to ensure that a black hole is actually present. For
two-dimensional dilaton gravity, and probably a much wider class of theories, I
show that the imposition of a spacelike ``stretched horizon'' constraint
modifies the algebra of symmetries, inducing a central term. Standard conformal
field theory techniques then fix the asymptotic density of states, reproducing
the Bekenstein-Hawking entropy. The states responsible for black hole entropy
can thus be viewed as ``would-be gauge'' states that become physical because
the symmetries are altered.
