  We catalogue the primitive ideals of the Cuntz-Krieger algebra of a
row-finite higher-rank graph with no sources. Each maximal tail in the vertex
set has an abelian periodicity group of finite rank at most that of the graph;
the primitive ideals in the Cuntz-Krieger algebra are indexed by pairs
consisting of a maximal tail and a character of its periodicity group. The
Cuntz-Krieger algebra is primitive if and only if the whole vertex set is a
maximal tail and the graph is aperiodic.
