  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]
