Using Far Ultraviolet Spectroscopic Explorer and Hubble Space Telescope observations of the QSO PG1259+593, we detect D I Lyman-series absorption in high velocity cloud Complex C, a low-metallicity gas cloud falling onto the Milky Way. This is the first detection of atomic deuterium in the local universe in a location other than the nearby regions of the Galactic disk. A new Westerbork Synthesis Radio Telescope (WSRT) interferometer map of the H I 21 cm emission toward PG1259+593 indicates that the sight line passes through a compact concentration of neutral gas in Complex C. We find D/H = (2.2+/-0.7)x10^-5, O/H = (8.0+/-2.5)x10^-5, and D/O = 0.28+/-0.12. The metallicity of Complex C gas toward PG1259+593 is approximately 1/6 solar, as inferred from the oxygen abundance [O/H] = -0.79 (+0.12, -0.16). While we cannot rule out a value of D/H similar to that found for the local ISM, we can confidently exclude values as low as those determined recently for extended sight lines in the Galactic disk. Combined with the sub-solar metallicity estimate and the low nitrogen abundance, this conclusion lends support to the hypothesis that Complex C is located outside the Milky Way, rather than inside in material recirculated between the Galactic disk and halo. The value of D/H for Complex C is consistent with the primordial abundance of deuterium inferred from recent Wilkinson Microwave Anisotropy Probe observations of the cosmic microwave background and simple chemical evolution models that predict the amount of deuterium astration as a function of metallicity. [Abbreviated abstract]
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