We present an X-ray study of the three most metal-deficient blue compact dwarf (BCD) galaxies known in the local Universe, based on deep Chandra observations of SBS 0335-052 (0.025 solar abundance), SBS 0335-052W (0.02 solar abundance) and I Zw 18 (0.02 solar abundance). All three are detected, with more than 90% of their X-ray emission arising from point-like sources. The 0.5-10.0 keV luminosities of these point sources are in the range (1.3-8.5)x1e39 erg/s. We interpret them to be single or a collection of high-mass X-ray binaries, the luminosities of which may have been enhanced by the low metallicity of the gas. There are hints of faint extended diffuse X-ray emission in both SBS 0335-052 and I Zw 18, probably associated with the superbubbles visible in both BCDs. The spectrum of I Zw 18 shows a OVIII hydrogen-like emission line. The best spectral fit gives an O overabundance of the gas in the X-ray point source by a factor of ~7 with respect to the Sun, or a factor of ~350 with respect to the O abundance determined for the HII region.
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