  We investigate boundary conditions for the nonlinear sigma model on the
compact symmetric space $G/H$, where $H \subset G$ is the subgroup fixed by an
involution $\sigma$ of $G$. The Poisson brackets and the classical local
conserved charges necessary for integrability are preserved by boundary
conditions in correspondence with involutions which commute with $\sigma$.
Applied to $SO(3)/SO(2)$, the nonlinear sigma model on $S^2$, these yield the
great circles as boundary submanifolds. Applied to $G \times G/G$, they
reproduce known results for the principal chiral model.
