We analyze the outage capacity performance of the Massive MIMO uplink in a random line-of-sight (LoS) scenario. Considering a maximum-ratio combining receiver and assuming perfect channel state information at the base station (BS), we derive closed-form expressions for a lower bound on the outage capacity. It is shown that the outage capacity of Massive MIMO in the random LoS scenario logarithmically increases with the number of BS antennas due to the fact that the fluctuations in the total interference power become negligible (i.e., an interference hardening effect).