  It is shown that the general solution of classical equations of motion in two
dimensional dilaton gravity proposed by Callan, Giddings, Harvey and Strominger
(CGHS) includes a Lorentzian wormhole solution in addition to a black hole
solution. We also show that matter perturbation of the wormhole by a shock wave
leads to the formation of a black hole where the curvature singularity is
cloaked by the global event horizon. It is also argued that the classical
wormhole would be stable against quantum corrections.
