  We present a static solution for $d = 2$ critical string theory including the
tachyon $T$ but not its potential $V(T)$. This solution thus incorporates
tachyon back reaction and, when $T = 0$, reduces to the black hole solution.
When $T \neq 0$ one finds that (1) the Schwarzschild horizon of the above black
hole splits into two, resembling Reissner-Nordstrom horizons and (2) the
curvature scalar develops new singularities at the horizons. These features, as
we argue, will persist even with $V(T)$ present. Some possible methods for
removing these singularities are discussed.
