Spectroscopy of the low-mass X-ray binary Ser X-1 using the Gran Telescopio Canarias have revealed a ≃2 h periodic variability that is present in the three strongest emission lines. We tentatively interpret this variability as due to orbital motion, making it the first indication of the orbital period of Ser X-1. Together with the fact that the emission lines are remarkably narrow, but still resolved, we show that a main-sequence K dwarf together with a canonical 1.4 M⊙ neutron star gives a good description of the system. In this scenario, the most likely place for the emission lines to arise is the accretion disc, instead of a localized region in the binary (such as the irradiated surface or the stream-impact point), and their narrowness is due instead to the low inclination (≤10°) of Ser X-1.