We have produced laser-cooled crystals of (232)Th(3+) in a linear rf Paul trap. This is the first time that a multiply charged ion has been laser cooled. Our work opens an avenue for excitation of the nuclear transition in a trapped, cold (229)Th(3+) ion. Laser excitation of nuclear states would establish a new bridge between atomic and nuclear physics, with the promise of new levels of metrological precision.