  The parity-conserving $a$ and parity-violating $b$ amplitudes for weak
radiative hyperon decay are studied using chiral perturbation theory. The
imaginary parts of $a$ and $b$ are computed using unitarity. The real part of
$b$ is dominated by a one-loop infrared divergent graph which is computed. The
real part of $a$ has a large theoretical uncertainty and cannot be calculated
reliably. Counterterms for the $a$ and $b$ amplitudes are classified using
$CPS$ symmetry. The experimental values for decay widths and asymmetries are
consistent with theory, with the exception of the asymmetry parameter for the
$\Sigma^+ \rightarrow p \gamma$ decay.
