X-rays from binaries in small, metal-deficient galaxies may have contributed significantly to the heating and reionization of the early Universe. We investigate this claim by studying blue compact dwarfs (BCDs) as local analogues to these early galaxies. We constrain the relation of the X-ray luminosity function (XLF) to the star formation rate (SFR) using a Bayesian approach applied to a sample of 25 BCDs. The functional form of the XLF is fixed to that found for near-solar metallicity galaxies and is used to find the probability distribution of the normalization that relates X-ray luminosity to SFR. Our results suggest that the XLF normalization for low-metallicity BCDs (12+log(O/H) < 7.7) is not consistent with the XLF normalization for galaxies with near-solar metallicities, at a confidence level 1-5 × 10− 6. The XLF normalization for the BCDs is found to be $14.5\pm 4.8\ (\rm{M}_{\odot }^{-1}\, {\rm yr})$ , a factor of 9.7 ± 3.2 higher than for near-solar metallicity galaxies. Simultaneous determination of the XLF normalization and power-law index result in estimates of $q = 21.2^{+12.2}_{-8.8}\ (\rm{M}_{\odot }^{-1}\, {\rm yr})$ and $\alpha = 1.89^{+0.41}_{-0.30}$ , respectively. Our results suggest a significant enhancement in the population of high-mass X-ray binaries in BCDs compared to the near-solar metallicity galaxies. This suggests that X-ray binaries could have been a significant source of heating in the early Universe.