  A $\theta$ term, which couples to topological charge, is added to the lattice
$CP^{N-1}$ model. The strong-coupling character expansion is developed. The
series for the free energy and mass gap are respectively computed to tenth
order and fourth order. Several features of the strong-coupling analysis
emerge. One is the loss of superconfinement. Another is that in the
intermediate coupling constant region, there are indications of a transition to
a deconfining phase when $\theta$ is sufficiently large. The transition is like
the one which has been observed in Monte Carlo simulations of a similar lattice
$CP^{N-1}$ action.
