  We identify and compute the main corrections to $R_b$ in Topcolor theories.
They are due to the top-pions, the pseudo-Goldstone bosons associated with the
chiral symmetry breaking responsible for the top quark mass, and amount to
-(1-4)%, independent of the details of the Topcolor model. We show that the
cancellation of this effect against the contributions from Topcolor vector and
scalar resonances is unlikely, given the inherently distinct character of the
two scales governing the potentially cancelling terms. The resulting value of
$R_b$ leads to severe constraints on Topcolor theories.
