The determination of fundamental parameters in low-mass X-ray binaries 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 low-mass X-ray binary (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, constrained the mass of the secondary and the orbital inclination of the binary system . These values are consistent with previous estimates from independent methods. Via the same technique, the next generation of X-ray observatories equipped with high spec- tral 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.