We present high-quality spectroscopic observations of the two most-metal deficient blue compact galaxies known, I Zw 18 and SBS 0335-052 to determine the helium abundance. The underlying stellar absorption strongly influences the observed intensities of He I emission lines in the brightest NW component of I Zw 18, and hence this component should not be used for primordial He abundance determination. The effect of underlying stellar absorption, though present, is much smaller in the SE component. Assuming all systematic uncertainties are negligible, the He mass fraction derived in this component is Y = 0.243+/-0.007. The high signal-to-noise ratio spectrum (> 100 in the continuum) of SBS 0335-052 allows us to measure the helium mass fraction with a precision better than 2% -- 5% in nine different regions along the slit. Assuming all systematic uncertainties are negligible, the weighted mean He mass fraction in SBS 0335-052 is Y = 0.2437+/-0.0014 when the three He I 4471, 5876 and 6678 emission lines are used, and is 0.2463+/-0.0015 when the He I 4471 emission line is excluded. The weighted mean helium mass fraction in the two most metal-deficient BCGs I Zw 18 and SBS 0335-052, Y=0.2462+/-0.0015, after correction for the stellar He production results in a primordial He mass fraction Yp = 0.2452+/-0.0015. The derived Yp leads to a baryon-to-photon ratio of (4.7+/-1.0) 10^{-10}, consistent with the values derived from the primordial D and 7Li abundances, and supporting the standard big bang nucleosynthesis theory. For the most consistent set of primordial D, 4He, and 7Li abundances we derive an equivalent number of light neutrino species 3.0+/-0.3 (95% C.L.).
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