Phase-resolved high-resolution optical spectroscopy has revealed narrow NIII and HeII emission lines from the soft X-ray transient Aquila X-1 during its 2004 outburst that move as a function of the orbit consistent with the phasing of the donor star. Under the assumption that these lines come from the irradiated side of the donor star, we can constrain its K2 velocity to >=247 +/- 8 kms-1 and derive a mass function of f(M1) >= 1.23 +/- 0.12Msolar. Estimates for the rotational broadening based on the emission components suggest a possible massive neutron star of >=1.6Msolar (at 95 per cent confidence). However, an updated ephemeris and additional high-resolution spectroscopy of AqlX-1 during a future outburst are warranted in order to confirm that the narrow lines indeed originate on the donor star surface, and reliably characterize the system parameters of this important X-ray binary. Spectra taken during the end of the outburst show that the morphology of the emission lines changed dramatically. No donor star signature was present anymore, while the presence of narrow low-velocity emission lines became clear, making AqlX-1 a member of the slowly growing class of low-velocity emission-line sources. Based on data collected at the European Southern Observatory Paranal, Chile (Obs Id 073.D-0819). E-mail: corneli [at] iac.es (corneli[at]iac[dot]es)