  In this note, we consider the Dirac operator $D$ on a Riemannian symmetric
space $M$ of noncompact type. Using representation theory we show that $D$ has
point spectrum iff the $\hat A$-genus of its compact dual does not vanish. In
this case, if $M$ is irreducible then $M = U(p,q)/U(p) \times U(q)$ with $p+q$
odd, and $Spec_p(D) = \{0\}$.
