Within the standard models of particle physics and cosmology we have calcul
ated the big-bang prediction for the primordial abundance of He-4 to a theo
retical uncertainty of less than 0.1% (delta Y-P < +/-0.0002), improving th
e current theoretical precision by a factor of 10. At this accuracy the unc
ertainty in the abundance is dominated by the experimental uncertainty in t
he neutron mean lifetime, tau(n) = 885.4 +/- 2.0 sec. The following physica
l effects were included in the calculation: the zero and finite-temperature
radiative, Coulomb and finite-nucleon-mass corrections to the weak rates;
order-alpha quantum-electrodynamic correction to the plasma density, electr
on mass, and neutrino temperature; and incomplete neutrino decoupling. New
results for the finite-temperature radiative correction and the QED plasma
correction were used. In addition, we wrote a new and independent nucleosyn
thesis code designed to control numerical errors to be less than 0.1%. Our
predictions for the He-4 abundance are presented in the form of an accurate
fitting formula. Summarizing our work in one number, Y-P(eta = 5 X 10(-10)
) = 0.2462 +/- 0.0004 (expt) +/- <0.0002 (theory). Further, the baryon dens
ity inferred from the Burles-Tytler determination of the primordial D abund
ance, Omega(B)h(2) = 0.019 +/- 0.001, leads to the prediction Y-P = 0.2464
+/- 0.0005 (D/H) +/- <0.0002 (theory) +/-0.0005 (expt). This "prediction" a
nd an accurate measurement of the primeval He-4 abundance will allow an imp
ortant consistency test of primordial nucleosynthesis. [S0556-2821(99)05106
-1].