  We present Keck/MOSFIRE observations of the role of environment in the
formation of galaxies at z~2. Using K-band spectroscopy of H-alpha and [N II]
emission lines, we have analyzed the metallicities of galaxies within and
around a z=2.3 protocluster discovered in the HS1700+643 field. Our main sample
consists of 23 protocluster and 20 field galaxies with estimates of stellar
masses and gas-phase metallicities based on the N2 strong-line metallicity
indicator. With these data we have examined the mass-metallicity relation (MZR)
with respect to environment at z~2. We find that field galaxies follow the
well-established trend between stellar mass and metallicity, such that more
massive galaxies have larger metallicities. The protocluster galaxies, however,
do not exhibit a dependence of metallicity on mass, with the low-mass
protocluster galaxies showing an enhancement in metallicity compared to field
galaxies spanning the same mass range. A comparison with galaxy formation
models suggests that the mass-dependent environmental trend we observed can be
qualitatively explained in the context of the recycling of "momentum-driven"
galaxy wind material. Accordingly, winds are recycled on a shorter timescale in
denser environments, leading to an enhancement in metallicity at fixed mass for
all but the most massive galaxies. Future hydrodynamical simulations of z~2
overdensities matching the one in the HS1700 field will be crucial for
understanding the origin of the observed environmental trend in detail.
