We study the mass-metallicity relation at high redshift (z ≳ 2) using a sample of 87 star-forming galaxies with mean spectroscopic redshift ⟨z⟩ = 2.26 ± 0.17. Using stellar masses derived from spectral energy distribution fitting to U_nGRJK_s (and Spitzer IRAC, for 37% of the sample) photometry, we divide the sample into six stellar mass bins and construct six composite Hα + [N II] spectra. We estimate the mean oxygen abundance in each bin from the [N II]/Hα ratio and find a monotonic increase in metallicity with stellar mass, from 12 + log(O/H) < 8.2 for galaxies with ⟨M*⟩ = 2.7 × 10⁹ M☉ to 12 + log(O/H) = 8.6 for galaxies with ⟨M*⟩ = 1.0 × 10¹¹ M☉. The mass-metallicity relation at z ∼ 2 is offset from the local relation by ~0.3 dex, indicating lower metallicities at high redshift for galaxies of the same stellar mass. A corresponding metallicity-luminosity relation shows no significant correlation, explained by large variations in the rest-frame optical mass-to-light ratio at z ∼ 2. We estimate gas fractions using the empirical relation between star formation rate density and gas density, finding an increase in gas fraction with decreasing stellar mass. The median gas fraction is more than twice that of local star-forming galaxies, explaining the lower metallicities at z ∼ 2. Combining gas fractions with observed metallicities allows estimation of the effective yield y_eff as a function of stellar mass, showing a slight increase with stellar mass. This variation is best fit by a model with supersolar yield and outflow rate ~4 times higher than the star formation rate. The mass-metallicity relation at high redshift is driven by increasing metallicity as gas fraction decreases through star formation, likely modulated by metal loss from strong outflows. Our ability to detect differential metal loss is limited by the small range of baryonic masses in the sample, but there is no evidence for preferential loss from low mass galaxies. Subject headings: galaxies: abundances—galaxies: evolution—galaxies: high-redshift.We study the mass-metallicity relation at high redshift (z ≳ 2) using a sample of 87 star-forming galaxies with mean spectroscopic redshift ⟨z⟩ = 2.26 ± 0.17. Using stellar masses derived from spectral energy distribution fitting to U_nGRJK_s (and Spitzer IRAC, for 37% of the sample) photometry, we divide the sample into six stellar mass bins and construct six composite Hα + [N II] spectra. We estimate the mean oxygen abundance in each bin from the [N II]/Hα ratio and find a monotonic increase in metallicity with stellar mass, from 12 + log(O/H) < 8.2 for galaxies with ⟨M*⟩ = 2.7 × 10⁹ M☉ to 12 + log(O/H) = 8.6 for galaxies with ⟨M*⟩ = 1.0 × 10¹¹ M☉. The mass-metallicity relation at z ∼ 2 is offset from the local relation by ~0.3 dex, indicating lower metallicities at high redshift for galaxies of the same stellar mass. A corresponding metallicity-luminosity relation shows no significant correlation, explained by large variations in the rest-frame optical mass-to-light ratio at z ∼ 2. We estimate gas fractions using the empirical relation between star formation rate density and gas density, finding an increase in gas fraction with decreasing stellar mass. The median gas fraction is more than twice that of local star-forming galaxies, explaining the lower metallicities at z ∼ 2. Combining gas fractions with observed metallicities allows estimation of the effective yield y_eff as a function of stellar mass, showing a slight increase with stellar mass. This variation is best fit by a model with supersolar yield and outflow rate ~4 times higher than the star formation rate. The mass-metallicity relation at high redshift is driven by increasing metallicity as gas fraction decreases through star formation, likely modulated by metal loss from strong outflows. Our ability to detect differential metal loss is limited by the small range of baryonic masses in the sample, but there is no evidence for preferential loss from low mass galaxies. Subject headings: galaxies: abundances—galaxies: evolution—galaxies: high-redshift.