The performance of multi-user massive multiple-input multiple-output orthogonal frequency division multiplexing uplink systems in the presence of base station (BS) phase noise impairments is investigated. Closed-form achievable rate expressions are rigorously derived under two different operations, namely, the case of a common oscillator (synchronous operation) at the BS and the case of independent oscillators at each BS antenna (non-synchronous operation). It is observed that the non-synchronous operation exhibits superior performance due to the averaging of a portion of the intercarrier interference. Furthermore, radiated power scaling laws are derived, which are identical to the phase-noise-free case.