  We show that the one-instanton sector moduli-space divergence of the O(3)
Sigma Model leads to an unacceptable dependence of Green's functions on the
arbitrary way that the field is split into a quantum fluctuation about a
classical background. Since the divergence is associated with the degeneration
of field configurations to those of the zero-instanton sector this
arbitrariness may be cancelled by a `topological counter-term' which we
construct.
