We report the results of an analysis of high-quality spectroscopic and photometric observations of 18 giants in NGC 3201. We have included alpha Boo and the cool metal-poor field star HDE 232078 as comparison objects. We find evidence of a significant extinction gradient across the cluster with a range in E(B-V) of about 0.1 mag, which has not been taken into account in previous studies. The mean value of [Fe/H] for the cluster is -1.42 +/- 0.03 (sigma = 0.14). The Na and Al abundances correlate with each other and anticorrelate with the O abundances in a pattern similar to that reported recently for other globular clusters. The [O/H], [Na/H], and [Al/H] values range from -1.5 to -0.8, -0.7 to -1.5, and -0.5 to -1.5, respectively. The alpha-elements (even-even nuclei from Mg to Ti) show the usual excess relative to iron for metal-poor stars. The heavy-element abundance patterns are dominated by contributions from an r-process reservoir. The relative s-process contribution to the NGC 3201 giants is less than or equal to that in alpha Boo, and it is significantly less than in the Sun. In contrast, the relative s-process contribution to the halo star HDE 232078 is nearly as large as in the Sun. There is a hint that the relative r- and s-process contributions correlate with the O abundance (in the sense that the low-O stars have a larger relative s-process component). Lee 1312, the star for which our analysis is most complete, has a very similar distribution of s-process species, as does alpha Boo. Although NGC 3201 has an unusual Galactic orbit, we find no new evidence from our analysis that it is a captured cluster.