The first application, to our knowledge, of an all-solid-state system of lasers to the study of a single cooled trapped Sr(+) ion is described. Quantum jumps have been observed by driving the 674-nm 5s(2)S(1/2)-4d(2)D(5/2) transition, and preliminary observations of the line shape are reported. An upper limit for the temperature of a single ion, derived from the 674-nm linewidth, was 200 mK. If non-Doppler sources of broadening such as unresolved Zeeman structure dominate, then the temperature limit would be even lower.