We will present detailed constraints on the metallicity dependence of the high mass X-ray binary (HMXB) X-ray luminosity function (XLF). We analyze ~5 Ms of Chandra data for 55 actively star-forming galaxies at D < 30 Mpc with gas-phase metallicities spanning 12 + log(O/H) ~ 7-9.2. Within the galactic footprints, our sample contains a total of 1311 X-ray point sources. We construct a model that successfully characterizes the average HMXB XLF over the full metallicity range. We demonstrate that the SFR-normalized HMXB XLF shows clear trends with metallicity, changing in both shape and normalization across the full metallicity range. Our model provides a revised scaling relation of integrated LX /SFR versus 12 + log(O/H) and a new characterization of its the SFR-dependent stochastic scatter. We compare our trends with past studies based on integrated galaxy emission and discuss the source populations that drive these integrated relations. Our results have implications for binary population synthesis models, the nature of super-Eddington accreting objects (e.g., ultraluminous X-ray sources), recent efforts to identify active galactic nucleus candidates in dwarf galaxies, and the X-ray radiation fields in the early Universe during the epoch of cosmic heating at z > 10.