  We describe a static solution for $d = 2$ critical string theory including
the tachyon $T$ but with its potential $V (T)$ set to zero. This solution thus
incorporates tachyon back reaction and, when $T = 0$, reduces to the black hole
solution. When $T \neq 0$ we find 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. We show
that these features will persist even when $V (T)$ is nonzero. We present a
time dependent extension of our static solution and discuss some possible
methods for removing the above singularities.
