  The MEarth Project is a photometric survey systematically searching the
smallest stars nearest to the Sun for transiting rocky planets. Since 2008,
MEarth has taken approximately two million images of 1844 stars suspected to be
mid-to-late M dwarfs. We have augmented this survey by taking nightly exposures
of photometric standard stars and have utilized this data to photometrically
calibrate the $MEarth$ system, identify photometric nights, and obtain an
optical magnitude with $1.5\%$ precision for each M dwarf system. Each optical
magnitude is an average over many years of data, and therefore should be
largely immune to stellar variability and flaring. We combine this with
trigonometric distance measurements, spectroscopic metallicity measurements,
and 2MASS infrared magnitude measurements in order to derive a
color-magnitude-metallicity relation across the mid-to-late M dwarf spectral
sequence that can reproduce spectroscopic metallicity determinations to a
precision of 0.1 dex. We release optical magnitudes and metallicity estimates
for 1567 M dwarfs, many of which did not have an accurate determination of
either prior to this work. For an additional 277 stars without a trigonometric
parallax, we provide an estimate of the distance assuming solar neighborhood
metallicity. We find that the median metallicity for a volume limited sample of
stars within 20 parsecs of the Sun is [Fe/H] = $-0.03 \pm 0.008$, and that 29 /
565 of these stars have a metallicity of [Fe/H] = $-0.5$ or lower, similar to
the low-metallicity distribution of nearby G-dwarfs. When combined with the
results of ongoing and future planet surveys targeting these objects, the
metallicity estimates presented here will be important in assessing the
significance of any putative planet-metallicity correlation.
