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 . In this paper , 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 } \gtrsim 10 ^ { 39 } erg s ^ { -1 } ; 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 \approx 4 times more L _ { X } > 10 ^ { 40 } erg s ^ { -1 }  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 normalizations and bright-end slopes until we reproduce the observed point source luminosity distributions . We find that these LBAs have a shallower bright end slope ( \gamma _ { 2 } = 1.90 ) than the standard XLF ( \gamma _ { 2 } = 2.73 ) . If we conservatively assume that the brightest X-ray source from each galaxy is powered by an accreting supermassive black hole 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 .