  The M31 globular cluster X-ray binary XB158 (a.k.a. Bo 158) exhibits
intensity dips on a 2.78 hr period in some observations, but not others. The
short period suggests a low mass ratio, and an asymmetric, precessing disk due
to additional tidal torques from the donor star since the disk crosses the 3:1
resonance. Previous theoretical 3D smoothed particle hydrodynamical modeling
suggested a super-orbital disk precession period 29$\pm$1 times the orbital
period, i.e. $\sim$81$\pm$3 hr. We conducted a Swift monitoring campaign of 30
observations over ~1 month in order to search for evidence of such a
super-orbital period. Fitting the 0.3--10 keV Swift XRT luminosity lightcurve
with a sinusoid yielded a period of 5.65+/-0.05 days, and a >5$\sigma$
improvement in $\chi^2$ over the best fit constant intensity model. A
Lomb-Scargle periodogram revealed that periods 5.4--5.8 days were detected at a
>3$\sigma$ level, with a peak at 5.6 days. We consider this strong evidence for
a 5.65 day super-orbital period, ~70\% longer than the predicted period. The
0.3--10 keV luminosity varied by a factor ~5, consistent with variations seen
in long-term monitoring from Chandra. We conclude that other X-ray binaries
exhibiting similar long-term behaviour are likely to also be X-ray binaries
with low mass ratios and super-orbital periods.
