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We report the detection of a 78.1 ± 0.5 day period in the X-ray light curve of the extreme ultraluminous X-ray source NGC 5907 ULX1 (L$_\text{X,peak}$ ~ 5 × 10$^{40}$ erg s$^{-1}$), discovered during an extensive monitoring program with $\textit{Swift}$. These periodic variations are strong, with the observed flux changing by a factor of ~3-4 between the peaks and the troughs of the cycle; our simulations suggest that the observed periodicity is detected comfortably in excess of 3$\sigma$ significance. We discuss possible origins for this X-ray period, but conclude that at the current time we cannot robustly distinguish between orbital and super-orbital variations., A.C.F. acknowledges support from ERC Advanced Grant 340442. The work of D.J.W./D.S. was performed at JPL/Caltech, under contract with NASA. D.B. and N.W. acknowledge financial support from the French Space Agency (CNES), M.J.M. acknowledges support from an Ernest Rutherford STFC fellowship, and T.P.R. acknowledges support from the STFC consolidated grant ST/L00075X/1. This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester, and also made use of the XRT Data Analysis Software (XRTDAS) developed under the responsibility of the ASI Science Data Center (ASDC), Italy. We acknowledge the use of public data from the Swift data archive. This research has also made use of a collection of ISIS functions (ISISscripts) provided by ECAP/Remeis observatory and MIT.