We report the discovery of deuterium absorption in the very metal-poor ([Fe/H] = -2.88) damped Lyman-alpha system at z_abs = 3.06726 toward the QSO SDSS J1358+6522. On the basis of 13 resolved D I absorption lines and the damping wings of the H I Lyman alpha transition, we have obtained a new, precise measure of the primordial abundance of deuterium. Furthermore, to bolster the present statistics of precision D/H measures, we have reanalyzed all of the known deuterium absorption-line systems that satisfy a set of strict criteria. We have adopted a blind analysis strategy (to remove human bias), and developed a software package that is specifically designed for precision D/H abundance measurements. For this reanalyzed sample of systems, we obtain a weighted mean of (D/H)_p = (2.53 +/- 0.04) x 10^-5, corresponding to a Universal baryon density100 Omega_b h^2 = 2.202 +/- 0.046 for the standard model of Big Bang Nucleosynthesis. By combining our measure of (D/H)_p with observations of the cosmic microwave background, we derive the effective number of light fermion species, N_eff = 3.28 +/- 0.28. We therefore rule out the existence of an additional (sterile) neutrino (i.e. N_eff = 4.046) at 99.3 percent confidence (2.7 sigma), provided that N_eff and the baryon-to-photon ratio (eta_10) did not change between BBN and recombination. We also place a strong bound on the neutrino degeneracy parameter, xi_D = +0.05 +/- 0.13 based only on the CMB+(D/H)_p observations. Combining xi_D with the current best literature measure of Y_p, we find |xi| <= +0.062. In future, improved measurements of several key reaction rates, in particular d(p,gamma)3He, and further measures of (D/H)_p with a precision comparable to those considered here, should allow even more stringent limits to be placed on new physics beyond the standard model.
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