We report the discovery and analysis of the most metal-poor damped Lyman- \alpha ( DLA ) system currently known , which also displays the Lyman series absorption lines of neutral deuterium . The average [ O/H ] abundance of this system is [ O/H ] = -2.804 \pm 0.015 , which includes an absorption component with [ O/H ] = -3.07 \pm 0.03 . Despite the unfortunate blending of many weak D i absorption lines , we report a precise measurement of the deuterium abundance of this system . Using the six highest quality and self-consistently analyzed measures of D/H in DLAs , we report tentative evidence for a subtle decrease of D/H with increasing metallicity . This trend must be confirmed with future high precision D/H measurements spanning a range of metallicity . A weighted mean of these six independent measures provides our best estimate of the primordial abundance of deuterium , 10 ^ { 5 } ( { D / H } ) _ { P } = 2.547 \pm 0.033 ( \log _ { 10 } { ( D / H ) _ { P } } = -4.5940 \pm 0.0056 ) . We perform a series of detailed Monte Carlo calculations of Big Bang nucleosynthesis ( BBN ) that incorporate the latest determinations of several key nuclear cross sections , and propagate their associated uncertainty . Combining our measurement of ( D/H ) _ { P } with these BBN calculations yields an estimate of the cosmic baryon density , 100 \Omega _ { B, 0 } h ^ { 2 } ( { BBN } ) = 2.156 \pm 0.020 , if we adopt the most recent theoretical determination of the d ( p, \gamma ) ^ { 3 } \mathrm { He } reaction rate . This measure of \Omega _ { B, 0 } h ^ { 2 } differs by \sim 2.3 \sigma from the Standard Model value estimated from the Planck observations of the cosmic microwave background . Using instead a d ( p, \gamma ) ^ { 3 } \mathrm { He } reaction rate that is based on the best available experimental cross section data , we estimate 100 \Omega _ { B, 0 } h ^ { 2 } ( { BBN } ) = 2.260 \pm 0.034 , which is in somewhat better agreement with the Planck value . Forthcoming measurements of the crucial d ( p, \gamma ) ^ { 3 } \mathrm { He } cross section may shed further light on this discrepancy .