  We combine star-formation histories derived from observations of high
redshift galaxies with measurements of the z~0 relation between gas-phase
metallicity, stellar mass, and star formation rate to make an explicit and
completely empirical connection between near-field and distant galaxy
observations. Our approach relies on two basic assumptions: 1) galaxies'
average paths through time in stellar mass vs. star formation rate space are
represented by a family of smooth functions that are determined by the
galaxies' final stellar mass, and 2) galaxies grow and become enriched with
heavy elements such that they always evolve along the mass--metallicity--star
formation rate relation. By integrating over these paths, we can track the
chemical evolution of stars in galaxies in a model independent way, without the
need for explicit assumptions about gas inflow, outflow, or star formation
efficiency. Using this approach, we present predictions of stellar metallicity
(i.e., O/H) distribution functions for present day star-forming galaxies of
different stellar masses and the evolution of the alpha-element stellar
metallicity-mass relation since z~1. The metallicity distribution functions are
fairly well described as Gaussians, truncated at high metallicity, with
power-law tails to low metallicity. We find that the stellar metallicity
distribution for Milky Way mass galaxies is in reasonable agreement with
observations for our Galaxy, and that the predicted stellar mass vs. mean
stellar metallicity relation at z=0 agrees quite well with results derived from
galaxy surveys. This validates the assumptions that are implicit in our simple
approach. Upcoming observations will further test these assumptions and their
range of validity, by measuring the mean stellar mass-metallicity relation up
to z~1, and by measuring the stellar metallicity distributions over a range of
galaxy masses.
