We report the discovery of narrow X-ray absorption lines from the low-mass X-ray binary MXB1659-298 during an XMM-Newton observation in 2001 February. The 7.1 hr orbital cycle is clearly evident with narrow X-ray eclipses preceded by intense dipping activity. A sinusoid-like OM $B$-band modulation with a peak-to-peak modulation of 0.5 magnitude and a minimum coincident with the X-ray eclipse is visible. EPIC and RGS spectra reveal the presence of narrow resonant absorption features identified with OVIII 1s-2p, 1s-3p and 1s-4p, NeX 1s-2p, FeXXV 1s-2p, and FeXXVI 1s-2p transitions, together with a broad Fe emission feature at ~6.5 keV. The EWs of the Fe absorption features show no obvious dependence on orbital phase, even during dipping intervals. Previously, the only X-ray binaries known to exhibit narrow X-ray absorption lines were two superluminal jet sources and it had been suggested that these features are related to the jet formation mechanism. This now appears unlikely, and instead their presence may be related to the viewing angle of the system. The MXB1659-298 0.6--12 keV continuum is modeled using absorbed cutoff power-law and blackbody components. During dips the blackbody is more strongly absorbed than the power-law. The spectral shape of the 3.6% of 0.5--10 keV emission that remains during eclipses is consistent with that during non-dipping intervals.