  Static black holes in two-dimensional string theory can carry tachyon hair.
Configurations which are non-singular at the event horizon have non-vanishing
asymptotic energy density. Such solutions can be smoothly extended through the
event horizon and have non-vanishing energy flux emerging from the past
singularity. Dynamical processes will not change the amount of tachyon hair on
a black hole. In particular, there will be no tachyon hair on a black hole
formed in gravitational collapse if the initial geometry is the linear dilaton
vacuum. There also exist static solutions with finite total energy, which have
singular event horizons. Simple dynamical arguments suggest that black holes
formed in gravitational collapse will not have tachyon hair of this type.
