  Heavy quark symmetry predicts the value of $B \rightarrow D$ and $B
\rightarrow D^*$ transition matrix elements of the current $\bar c \gamma_\mu
(1 - \gamma_5)b$, at zero recoil (where in the rest frame of the $B$ the $D$ or
$D^*$ is also at rest). We use chiral perturbation theory to compute the
leading corrections to these predictions which are generated at low momentum,
below the chiral symmetry breaking scale.
