We study the visibility of the Lyα emission line during the epoch of reionization. Combining galactic outflow models with large-scale seminumeric simulations of reionization, we quantify the probability distribution function of the fraction of Lyα photons transmitted through the intergalactic medium (IGM), . Our study focuses on galaxies populating dark matter haloes with masses of Mhalo= 1010 M⊙ at z= 8.6, which is inspired by the recent reported discovery of a galaxy at z= 8.6 with strong Lyα line emission. For reasonable assumptions, we find that the combination of winds and reionization morphology results in per cent (50 per cent), for the majority of galaxies, even when the Universe is ∼80 per cent (60 per cent) neutral by volume. Thus, the observed strong Lyα emission from the reported z= 8.6 galaxy is consistent with a highly neutral IGM, and cannot be used to place statistically significant constraints on the volume-averaged neutral fraction of hydrogen in the IGM. We also investigate the implications of the recent tentative evidence for an observed decrease in the ‘Lyman alpha emitter fraction’ among drop-out galaxies between z= 6 and 7. If confirmed, we show that a rapid evolution in will be required to explain this observation via the effects of reionization.