The decoupling of data and control planes, as proposed for 5G networks, will enable the efficient implementation of multitier networks where user equipment (UE) nodes obtain coverage and connectivity through the top-tier macro-cells, and, at the same time, achieve high-throughput low-latency communication through lower tiers in the hierarchy. This paper considers a new architecture for such lower tiers, dubbed fog massive MIMO, where the UEs are able to establish high-throughput low-latency data links in a seamless and opportunistic manner, as they travel through a dense fog of high-capacity wireless infrastructure nodes, referred to as remote radio heads (RRHs). Traditional handover mechanisms in dense multicell networks inherently give rise to frequent handovers and pilot sequence re-assignments, incurring, as a result, excessive protocol overhead and significant latency. In the proposed fog massive MIMO architecture, UEs seamlessly and implicitly associate themselves to the most convenient RRHs in a completely autonomous manner. Each UE makes use of a unique uplink pilot sequence, and pilot contamination is mitigated by a novel coded "on-the-fly" pilot contamination control mechanism. We analyze the spectral efficiency and the outage probability of the proposed architecture via stochastic geometry, using some recent results on unique coverage in Boolean models, and provide a detailed comparison with respect to an idealized baseline massive MIMO cellular system, that neglects protocol overhead and latency due to explicit user-cell association. Our analysis, supported by extensive system simulation, reveals that there exists a "sweet spot" of the per-pilot user load (number of users per pilot), such that the proposed system achieves spectral efficiency close to that of an ideal cellular system with the minimum distance user-base station association and no pilot/handover overhead.