In order to understand the rates and properties of Type Ia and Type Ib/c supernovae, X-ray binaries, gravitational wave sources, and gamma-ray bursts as a function of galactic environment and cosmic age, it is imperative that we measure how the close binary properties of O- and B-type stars vary with metallicity. We have studied eclipsing binaries with early B main-sequence primaries in three galaxies with different metallicities: the Large and Small Magellanic Clouds (LMC and SMC, respectively) and the Milky Way (MW). The observed fractions of early B stars that exhibit deep eclipses 0.25 2/M 1 > 0.1, (2) an intrinsic orbital period distribution slightly skewed toward shorter periods relative to a distribution that is uniform in log P, (3) a mass-ratio distribution weighted toward low-mass companions, and (4) a small, nearly negligible excess fraction of twins with q > 0.9. Our fitted parameters derived for the MW eclipsing binaries match the properties inferred from nearby, early-type spectroscopic binaries, which further validates our results. There are no statistically significant trends with metallicity, demonstrating that the close binary properties of massive stars do not vary across metallicities –0.7 > 0.1, (2) an intrinsic orbital period distribution slightly skewed toward shorter periods relative to a distribution that is uniform in log P, (3) a mass-ratio distribution weighted toward low-mass companions, and (4) a small, nearly negligible excess fraction of twins with q > 0.9. Our fitted parameters derived for the MW eclipsing binaries match the properties inferred from nearby, early-type spectroscopic binaries, which further validates our results. There are no statistically significant trends with metallicity, demonstrating that the close binary properties of massive stars do not vary across metallicities –0.7 ?) < 0.0 beyond the measured uncertainties.