  We report the detection of a $78.1\pm0.5$ day period in the X-ray lightcurve
of the extreme ultraluminous X-ray source NGC 5907 ULX1
($L_{\rm{X,peak}}\sim5\times10^{40}$ erg s$^{-1}$), discovered during an
extensive monitoring program with Swift. These periodic variations are strong,
with the observed flux changing by a factor of $\sim$3-4 between the peaks and
the troughs of the cycle; our simulations suggest that the observed periodicity
is detected comfortably in excess of 3$\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.
