We report new metallicity determinations for 39 red giants in a 220 arcmin2 region, 18 southwest of the bar of the Large Magellanic Cloud. These abundance measurements are based on spectroscopy of the Ca II infrared triplet. We have carefully considered the effects of abundance ratios, the physics of Ca II line formation, the variation of red clump magnitude, and the contamination by foreground stars in our abundance analyses. The metallicity distribution function (MDF) shows a strong peak at [Fe/H] = -0.57 ± 0.04; a tail to abundances at least as low as [Fe/H] ≈ -1.6 brings the average abundance down to [Fe/H] = -0.64 ± 0.02. Half the red giants in our field fall within the range -0.83 ≤ [Fe/H] ≤ -0.41. The MDF appears to be truncated at [Fe/H] ≈ -0.25; the exact value of the maximum abundance is subject to ~0.1 dex uncertainty in the calibration of the Ca II IR triplet for young, metal-rich stars. We find a striking contrast in the shape of the MDF below [Fe/H] ≤ -1 between our inner disk field and the distant outer field studied by Olszewski: red giants deficient by more than a factor of 10 in heavy elements relative to the Sun are extremely scarce in the inner disk of the LMC. Our field star sample does not reproduce the full MDF of the LMC star clusters but seems similar to that of the intermediate-age (1–3 Gyr) clusters. We have also obtained abundance estimates using Strömgren photometry for ≈103 red giants in the same field. Photometry is the only practical way to measure abundances for the large numbers of stars necessary to lift age-metallicity degeneracy from our high-precision color-magnitude diagrams. The Strömgren measurements, which are sensitive to a combination of cyanogen and iron lines, correlate well with the Ca II measurements, but a metallicity-dependent offset is found. The offset may be due either to variations in the elemental abundance ratios due to galactic chemical evolution or to a metal-dependent mixing mechanism in RGB stars. An empirical relation between photometric and spectroscopic abundance estimates is derived. This will allow photometric abundance measurements to be placed on a consistent metallicity scale with spectroscopic metallicities, for very large numbers of stars.