Using high signal-to-noise echelle spectra of 3C 273 obtained with the Space Telescope Imaging Spectrograph ( resolution = 7 km s ^ { -1 } FWHM ) , we constrain the metallicities of two Ly \alpha clouds in the vicinity of the Virgo cluster . We detect C ii , Si ii , and Si iii absorption lines in the Ly \alpha absorber at z _ { abs } = 0.00530 . Previous observations with the Far Ultraviolet Spectroscopic Explorer have revealed Ly \beta - Ly \theta absorption lines at the same redshift , thereby accurately constraining the H i column density . We model the ionization of the gas and derive [ C/H ] = -1.2 ^ { +0.3 } _ { -0.2 } , [ Si/C ] = +0.2 \pm 0.1 , and log n _ { H } = -2.8 \pm 0.3 . The model implies a small absorber thickness , \sim 70 pc , and thermal pressure p / k \approx 40 cm ^ { -3 } K. It is most likely that the absorber is pressure confined by an external medium because gravitational confinement would require a very high ratio of dark matter to baryonic matter . Based on a sample of Milky Way sight lines in which carbon and silicon abundances have been reliably measured in the same interstellar cloud ( including new measurements presented herein ) , we argue that it is unlikely that the overabundance of Si relative to C is due to depletion onto dust grains . Instead , this probably indicates that the gas has been predominately enriched by ejecta from Type II supernovae . Such enrichment is most plausibly provided by an unbound galactic wind , given the absence of known galaxies within a projected distance of 100 kpc and the presence of galaxies capable of driving a wind at larger distances ( e.g. , H i 1225+01 ) . Such processes have been invoked to explain the observed abundances in the hot , X-ray emitting gas in Virgo . However , the sight line to 3C 273 is more than 10 ^ { \circ } away from the X-ray emission region . We also constrain the metallicity and physical conditions of the Virgo absorber at z _ { abs } = 0.00337 in the spectrum of 3C 273 based on detections of O vi and H i and an upper limit on C iv . If this absorber is collisionally ionized , the O vi/C iv limit requires T \gtrsim 10 ^ { 5.3 } K in the O vi-bearing gas . For either collisional ionization or photoionization , we find that [ O/H ] \gtrsim - 2.0 at z _ { abs } = 0.00337 .