By extrapolating to O/H = N/H = 0 the empirical correlations Y–O/H and Y–N/H defined by a relatively large sample of ∼ 45 Blue Compact Dwarfs (BCDs), we have obtained a primordial 4Helium mass fraction Y p=0.2443±0.0015 with dY/dZ=2.4±1.0. This result is in excellent agreement with the average Y p=0.2452±0.0015 determined in the two most metal-deficient BCDs known, I Zw 18 (Z ⊙/50) and SBS 0335–052 (Z ⊙/41), where the correction for He production is smallest. The quoted error (1σ) of ≲ 1% is statistical and does not include systematic effects. We examine various systematic effects including collisional excitation of hydrogen lines, ionization structure and temperature fluctuation effects, and underlying stellar He i absorption, and conclude that combining all systematic effects, our Y p may be underestimated by ∼ 2–4%. Taken at face value, our Y p implies a baryon-to-photon number ratio η=(4.7+1.0 −0.8)×10−10 and a baryon mass fraction Ωb h 2 100=0.017±0.005 (2σ), consistent with the values obtained from deuterium and Cosmic Microwave Background measurements. Correcting Y p upward by 2–4% would make the agreement even better.