Ultraluminous x-ray sources (ULXs) in nearby galaxies shine brighter than any x-ray source in our Galaxy. ULXs are usually modeled as stellar-mass black holes (BHs) accreting at very high rates or intermediate-mass BHs. We present observations showing that NGC 5907 ULX is instead an x-ray accreting neutron star (NS) with a spin period evolving from 1.43 seconds in 2003 to 1.13 seconds in 2014. It has an isotropic peak luminosity of [Formula: see text]1000 times the Eddington limit for a NS at 17.1 megaparsec. Standard accretion models fail to explain its luminosity, even assuming beamed emission, but a strong multipolar magnetic field can describe its properties. These findings suggest that other extreme ULXs (x-ray luminosity [Formula: see text] 10 erg second[Formula: see text]) might harbor NSs.
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