  Ultraluminous X-ray (ULX) pulsars are a new class of object powered by
apparent super-critical accretion onto magnetized neutron stars. Three sources
in this class identified so far; M82 X-2, NGC 5907 ULX-1 and NGC 7793 P13, have
been found to have two properties in common; $\sim1$-s spin periods, and for
NGC 5907 ULX-1 and NGC 7793 P13 periodic X-ray flux modulations on timescales
of $\sim60-80$ days. M82 X-2 resides in a crowded field that includes the ULX
M82 X-1 separated from X-2 by 5", as well as other bright point sources. A
60-day modulation has been observed from the region but the origin has been
difficult to identify; both M82 X-1 and X-2 have been suggested as the source.
In this paper we present the analysis of a systematic monitoring campaign by
Chandra, the only X-ray telescope capable of resolving the crowded field. From
a simple Lomb-Scargle periodogram analysis and a more sophisticated Gaussian
Process analysis we find that only X-2 exhibits a periodic signal around 60
days supporting previous claims that it is the origin. We also construct a
phase-averaged flux profile of the modulations from higher cadence Swift/XRT
data and find that the flux variations in the Chandra data are fully consistent
with the flux profile. Since the orbit of the neutron star and its companion is
known to be 2.5 days, the $\sim60$-day period must be super-orbital in origin.
The flux of the modulations varies by a factor of $\sim$100 from minimum to
maximum, with no evidence for spectral variations, making the origin difficult
to explain.
