The fission chain paradigm is used to analyze the underlying stochastic-ity of the neutron transport equation. The analysis is limited to one-group neutrons in an infinite, homogeneous medium, and is done in the generation and in the time-dependent descriptions but includes external sources and neutron precursors. We give general results for average values and characterize the validity of the deterministic, mean-value description with the variance of the underlying stochastic process. We analyze the stochastic behavior of the one-point kinetic model and give asymptotic expressions for mean values and variances. In the absence of sources, we have also analyzed the probability of extinction of the fission chain and proved classical results. In particular, we show that a critical system with a continuous supply of target nuclei cannot maintain a self-sustained fission chain. This result is shown to be true even in the presence of precursors. We prove, however, that an idealized thermal reactor, infinite in size, can maintain a semblance of a stationary distribution for as long as a day without external intervention.