  We calculate the boundary $S$ matrix for the open antiferromagnetic spin
$1/2$ isotropic Heisenberg chain with boundary magnetic fields. Our approach,
which starts from the model's Bethe Ansatz solution, is an extension of the
Korepin-Andrei-Destri method. Our result agrees with the boundary $S$ matrix
for the boundary sine-Gordon model with $\beta^2 \rightarrow 8\pi$ and with
``fixed'' boundary conditions.
