  We apply field theory methods to $\mbox{SU}(3)$ chains in the symmetric
representation, with $p$ boxes in the Young tableau, mapping them into a flag
manifold non-linear $\sigma$-model with a topological angle $\theta =2\pi p/3$.
Generalizing the Haldane conjecture, we argue that the models are gapped for
$p=3m$ but gapless for $p=3m\pm 1$ (for integer $m$), corresponding to a
massless phase of the $\sigma$-model at $\theta =\pm 2\pi /3$. We confirm this
with Monte Carlo calculations on the $\sigma$-model.
