During a search for coherent signals in the X-ray archival data of XMM-Newton, we discovered a modulation at 1.2 s in 3XMM J004301.4+413017 (3X J0043), a source lying in the direction of an external arm of M 31. This short period indicates a neutron star (NS). Between 2000 and 2013, the position of 3X J0043 was imaged by public XMM-Newton observations 35 times. The analysis of these data allowed us to detect an orbital modulation at 1.27 d and study the long-term properties of the source. The emission of the pulsar was rather hard (most spectra are described by a power law with $Gamma < 1$) and, assuming the distance to M 31, the 0.3-10 keV luminosity was variable, from $sim$$3times10^{37}$ to $2times10^{38}$ erg s$^{-1}$. The analysis of optical data shows that, while 3X J0043 is likely associated to a globular cluster in M 31, a counterpart with $Vgtrsim22$ outside the cluster cannot be excluded. Considering our findings, there are two main viable scenarios for 3X J0043: a peculiar low-mass X-ray binary, similar to 4U 1822-37 or 4U 1626-67, or an intermediate-mass X-ray binary resembling Her X-1. Regardless of the exact nature of the system, 3X J0043 is the first accreting NS in M 31 in which the spin period has been detected.
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