We use new UV and optical spectra and an archival Hubble Space Telescope Wide Field Planetary Camera 2 (HST-WFPC2) image to study the za ? ze absorber in the ze ? 0.20 QSO PKS 2135-147. The UV spectra, obtained with the Faint Object Spectrograph on HST, show strong za ? ze absorption lines of C IV, N V, O VI, Ly?, and Ly?. The za ? ze line profiles are resolved, with deconvolved FWHM of 270-450 km s-1. The Lyman decrement and the O VI and N V doublet ratios indicate that there are also narrower, optically thick line components, and there is evidence in the C IV and Ly? profiles for two blended components. Lower limits on the total column densities are of order 1015 cm-2 for all ions. The ~2:1 ratio of the C IV doublets suggests that the total C IV column density is near the lower limit. If the absorber is photoionized by the QSO and the derived relative columns in C IV and H I are roughly correct, then the metallicity must be at least solar. The location of the za ? ze absorber remains uncertain. The line redshifts indicate that the clouds have little radial motion (less than ?200 km s-1) with respect to the QSO. This small velocity shift could mean that the absorber is outside of the deep gravitational potential of the QSO and the host-galaxy nucleus. Two ~L* galaxies in a small cluster centered on PKS 2135-147 lie within 36 h-1 kpc projected distance and have redshifts consistent with causing or contributing to the za ? ze lines. The extensive halo of the QSO's host galaxy could also contribute. Calculations show that the QSO is bright enough to photoionize gas up to O VI in the low-density halos of the host and nearby cluster galaxies. Nonetheless, there is indirect evidence for absorption much nearer the QSO, namely (1) the derived high (albeit uncertain) metallicity; (2) the relatively strong N V absorption lines, which might be caused by a higher nitrogen abundance in the metal-rich gas; and (3) strong, lobe-dominated, steep-spectrum radio emission, which is known to correlate with a much higher incidence of (probably intrinsic) za ? ze lines. We propose that the C IV/N V/O VI line ratios can be used as a general diagnostic of intrinsic versus intervening absorption, as long as the line saturation effects are understood.