Paroxysmal nocturnal hemoglobinuria (PNH) is an acquired clonal blood disorder characterized by hemolysis and a high risk of thrombosis, that is due to a deficiency in several cell surface proteins that prevent complement activation. Its origin has been traced to a somatic mutation in the PIG-A gene within hematopoietic stem cells (HSC). However, to date the question of how this mutant clone expands in size to contribute significantly to hematopoiesis remains under debate. One hypothesis posits the existence of a selective advantage of PIG-A mutated cells due to an immune mediated attack on normal HSC, but the evidence supporting this hypothesis is inconclusive. An alternative (and simpler) explanation attributes clonal expansion to neutral drift, in which case selection neither favours nor inhibits expansion of PIG-A mutated HSC. Here we examine the implications of the neutral drift model by numerically evolving a Markov chain for the probabilities of all possible outcomes, and investigate the possible occurrence and evolution, within this framework, of multiple independently arising clones within the HSC pool. Predictions of the model agree well with the known incidence of the disease and average age at diagnosis. Notwithstanding the slight difference in clonal expansion rates between our results and those reported in the literature, our model results lead to a relative stability of clone size when averaging multiple cases, in accord with what has been observed in human trials. The probability of a patient harbouring a second clone in the HSC pool was found to be extremely low ([Formula: see text]). Thus our results suggest that in clinical cases of PNH where two independent clones of mutant cells are observed, only one of those is likely to have originated in the HSC pool.