Solutions of bosonic string theory are constructed which correspond to
four-dimensional black holes with axionic quantum hair. The basic bui
lding blocks are the renormalization group flows of the CP1 model with
a theta term and the SU(1,1)/U(1) WZW coset conformal field theory. H
owever the solutions are also found to have negative energy excitation
s, and are accordingly expected to decay to the vacuum.