Authors:Kipping et alAbstract:The analysis of Proxima Centauri's radial velocities recently led Anglada-Escud\'e et al. (2016) to claim the presence of a low mass planet orbiting the Sun's nearest star once every 11.2 days. Although the a-priori probability that Proxima b transits its parent star is just 1.5%, the potential impact of such a discovery would be considerable. Independent of recent radial velocity efforts, we observed Proxima Centauri for 12.5 days in 2014 and 31 days in 2015 with the MOST space telescope. We report here that we cannot make a compelling case that Proxima b transits in our precise photometric time series. Imposing an informative prior on the period and phase, we do detect a candidate signal with the expected depth. However, perturbing the phase prior across 100 evenly spaced intervals reveals one strong false-positive and one weaker instance. We estimate a false-positive rate of at least a few percent and a much higher false-negative rate of 20-40%, likely caused by the very high flare rate of Proxima Centauri. Comparing our candidate signal to HATSouth ground-based photometry reveals that the signal is somewhat, but not conclusively, disfavored (1-2 sigmas) leading us to argue that the signal is most likely spurious. We expect that infrared photometric follow-up could more conclusively test the existence of this candidate signal, owing to the suppression of flare activity and the impressive infrared brightness of the parent star.