We report the detection of Deuterium absorption at redshift 2.525659 towards Q1243+3047. We describe improved methods to estimate the Deuterium to Hydrogen abundance ratio (D/H) in absorption systems, including improved modeling of the continuum level, the Ly-alpha forest and the velocity structure of the absorption. Together with improved relative flux calibration, these methods give D/H = 2.42^+0.35_-0.25 x 10^-5 cm^-2 from our Keck-I HIRES spectra of Q1243+3047, where the error is from the uncertainty in the shape of the continuum level and the amount of D absorption in a minor second component. The measured D/H is likely the primordial value because the [O/H] = -2.79 +/- 0.05. This absorption system has a neutral Hydrogen column density of 19.73 +/- 0.04 cm^-2, it shows five D lines and is mostly ionized. The best estimate of the primordial D/H is 2.78^+0.44_-0.38 x 10^-5, from the log D/H values towards five QSOs. The dispersion in the five values is larger than we expect from their individual measurement errors and we suspect this is because some of these errors were underestimated. We observe a trend in D/H with neutral H column density that we also suspect is spurious. The D/H corresponds to a baryon-to-photon ratio ETA = 5.9 +/- 0.5 x 10^-10 and a cosmological baryon density Omega_b h^2 = 0.0214 +/- 0.0020 (9.3%) that agrees with values from the pre-MAP measurements of the anisotropy of the Cosmic Microwave Background.
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