  We show that there is a topological (Berry phase) term in the non-linear
$\sigma$ model description of the SO(5) spin chain. It distinguishes the linear
and projective representations of the SO(5) symmetry group, in exact analogy to
the well-known $\theta$-term of the SO(3) spin chain. The presence of the
topological term is due to the fact that $\pi_2(\frac{SO(5)}{SO(3)\times
SO(2)})= \mathbb{Z}$. We discuss the implication of our results on the spectra
of the SO(5) spin chain, and connect it with a recent solvable SO(5) spin model
which exhibits valence bond solid ground state and edge degeneracy.
