  We study the worldsheet reflection matrix of a string attached to a D-brane
in $AdS_5 \times S^5$. The D-brane corresponds to a maximal giant graviton and
it wraps an $S^3$ inside $S^5$. In the gauge theory, the open string is
described by a spin chain with boundaries. We study an open string with a large
SO(6) charge, which allows us to focus on one boundary at a time and to define
an asymptotic boundary reflection matrix. We consider two cases corresponding
to two possible relative orientations for the charges of the giant graviton and
the open string. Using the symmetries of the problem we compute the boundary
reflection matrix up to a phase. These matrices obey the boundary Yang Baxter
equation. A crossing equation is derived for the overall phase. We perform weak
coupling computations up to two loops and obtain results that are consistent
with integrability. Finally, we determine the phase factor at strong coupling
using classical solutions.
