We report the detection of coherent pulsations from the ultraluminous X-ray source (ULX) NGC 7793 P13. The ≈0.42 s nearly sinusoidal pulsations were initially discovered in broadband X-ray observations using XMM-Newton and NuSTAR taken in 2016. We subsequently also found pulsations in archival XMM-Newton data taken in 2013 and 2014. The significant (≫5σ) detection of coherent pulsations demonstrates that the compact object in P13 is a neutron star, and given the observed peak luminosity of ≈10⁴⁰ erg s⁻¹ (assuming isotropy), it is well above the Eddington limit for a 1.4 M⨀ accretor. This makes P13 the second ULX known to be powered by an accreting neutron star. The pulse period varies between epochs, with a slow but persistent spin-up over the 2013–2016 period. This spin-up indicates a magnetic field of B ≈ 1.5 × 10¹² G, typical of many Galactic accreting pulsars. The most likely explanation for the extreme luminosity is a high degree of beaming; however, this is difficult to reconcile with the sinusoidal pulse profile.