{A high-resolution, high signal-to-noise HIRES-Keck spectrum of APM 08279+5255 reveals a feature in the HI Lyalpha profile of the z_abs=3.514 absorber at the expected position of the corresponding DI Lyalpha line. The absorber shows a relatively simple velocity structure, with a major component detected in several metallic lines including CII, CIV, SiII, SiIII and Si IV. Modeling of the hydrogen column density with the minimum number of components yields (D)/(H)~ 1.5 x 10(-5) . However, a more complex structure for the hydrogen cloud with somewhat ad hoc components would allow a higher (D)/(H). The system has a very low metallicity with [Si/H] ~ -3.5 and [C/H] ~ -4.0 and is therefore representative of essentially unprocessed material, with a deuterium abundance close to the primordial value. The present analysis favours the low D/H value of (D)/(H) =3.39+/- 0.25 x 10(-5) measured towards QSO 1009+2956 and QSO 1937-1009 ocite{burles} (Burles & Tytler 1998a, 1998b) ocite{burles2} as the fiducial value of deuterium at high redshift.} The data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation.