  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.).
