The determination of fundamental parameters in low-mass X-ray binaries (LMXBs) typically relies on measuring the radial velocity curve of the companion star through optical or near-infrared spectroscopy. It was recently suggested that high resolution X-ray spectroscopy might enable a measurement of the radial velocity curve of the compact object by monitoring the Doppler shifts induced by the orbital motion of the disc wind or the disc atmosphere. We analysed a Chandra-HETG+NuSTAR soft state observation of MXB 1659-298, an eclipsing neutron star LMXB. We measured a radial velocity curve whose phase offset and semi-amplitude are consistent with the primary star. We derived the value for the semi-amplitude of the radial velocity for the compact object K1 = 89 ± 19 km s-1, constrained the mass of the secondary (0.3 M⊙ ≤ M2 ≤ 0.8 M⊙) and the orbital inclination of the binary system (73°≤ i≤77°). These values are consistent with previous estimates from independent methods. Via the same technique, the next generation of X-ray observatories equipped with high spectral resolution instruments (e.g. Athena) will have the potential to measure the radial velocity curve of the primary in high inclination X-ray binaries to an accuracy of a few per cent.