  Strings propagating in three-dimensional anti-de Sitter space with a
background antisymmetric tensor field are well understood, even at the quantum
level. Pure three-dimensional gravity with a negative cosmological constant is
potentially important because of the existence of black hole solutions and an
asymptotic conformal symmetry, but it is mysterious and surprisingly resistant
to analysis. In this letter, the two theories are related by a map on the
classical level. The map is obtained by gauge fixing the string completely,
like in a light cone gauge, and comparing the resulting constrained theory with
the boundary theory obtained from gravity by imposing the appropriate
asymptotic boundary conditions. The two theories are formally related as
different gauge fixings of the same gauge theory.
