We present a new approach to understanding star-to-star helium abundance variations within globular clusters. We begin with detailed radiation hydrodynamics simulations of cluster formation within giant molecular clouds, and investigate the conditions under which multiple populations could be created. Chemical enrichment occurs dynamically as the cluster is assembled. We test two extreme mechanisms for injection of enriched gas within the clusters, and find that realistic multiple populations can be formed in both mechanisms. The stochastic cluster formation histories are dictated by the inherent randomness of the timing and location of the formation of small clusters, which rapidly merge to build up the larger cluster, in combination with continual accretion of gas from the cloud. These cluster formation histories naturally produce a diversity of abundance patterns across the massive cluster population. We conclude that multiple populations are a natural outcome of the typical mode of star cluster formation.