We have studied high mass X-ray binary (HMXB) populations within two low-metallicity, starburst galaxies, Haro 11 and VV 114. These galaxies serve as analogs to high-redshift (z>2) Lyman break galaxies, and within the larger sample of Lyman break analogs (LBAs) are sufficiently nearby (<87 Mpc) to be spatially-resolved by Chandra. Previous studies of the X-ray emission in LBAs have found that the 2-10 keV luminosity per star formation rate (SFR) in these galaxies is elevated, potentially because of their low metallicities (12+log[O/H]= 8.3-8.4). Theoretically, the progenitors of XRBs forming in lower metallicity environments lose less mass from stellar winds over their lifetimes, producing more massive compact objects (i.e., neutron stars and black holes), and thus resulting in more numerous and luminous HMXBs per SFR. We have performed an in-depth study of the only two LBAs that have spatially-resolved 2-10 keV emission with Chandra to present the bright end of the X-ray luminosity distribution of HMXBs (L$_X>10^{39}$ erg/s; ultraluminous X-ray sources, ULXs) in these low-metallicity galaxies, based on 8 detected ULXs. Comparing with the star-forming galaxy X-ray luminosity function (XLF) presented by Mineo et al. (2012), Haro 11 and VV 114 host ~4 times more L$_X>10^{40}$ erg/s sources than expected given their SFRs. We simulate the effects of source blending from crowded lower luminosity HMXBs using the star-forming galaxy XLF and then vary the XLF shapes until we reproduce the observed point source luminosity distributions. We find that these LBAs have a shallower bright end slope than the standard XLF. If we conservatively assume that the brightest X-ray source from each galaxy is powered by an AGN rather than a HMXB and eliminate these sources from consideration, the luminosity distribution becomes poorly constrained but does appear to be consistent with a standard XLF. [Abridged]
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