  There is a well known correlation between the mass and metallicity of
star-forming galaxies. Because mass is correlated with luminosity, this
relation is often exploited, when spectroscopy is not available, to estimate
galaxy metallicities based on single band photometry. However, we show that
galaxy color is typically more effective than luminosity as a predictor of
metallicity. This is a consequence of the correlation between color and the
galaxy mass-to-light ratio and the recently discovered correlation between star
formation rate (SFR) and residuals from the mass-metallicity relation. Using
Sloan Digital Sky Survey spectroscopy of 180,000 nearby galaxies, we derive
"LZC relations," empirical relations between metallicity (in seven common
strong line diagnostics), luminosity, and color (in ten filter pairs and four
methods of photometry). We show that these relations allow photometric
metallicity estimates, based on luminosity and a single optical color, that are
50% more precise than those made based on luminosity alone; galaxy metallicity
can be estimated to within 0.05 - 0.1 dex of the spectroscopically-derived
value depending on the metallicity diagnostic used. Including color information
in metallicity estimates also reduces systematic biases for populations skewed
toward high or low SFR environments, as we illustrate using the host galaxy of
the supernova SN 2010ay. This new tool will lend more statistical power to
studies of galaxy populations, such as supernova and gamma-ray burst (GRB) host
environments, in ongoing and future wide field imaging surveys.
