Chromist algae include diverse photosynthetic organisms of great ecological and social importance. Despite vigorous research efforts, a clear understanding of how various chromists acquired photosynthetic organelles has been complicated by conflicting phylogenetic results, along with an undetermined number and pattern of endosymbioses, and the horizontal movement of genes that accompany them. We apply novel statistical approaches to assess impacts of endosymbiotic gene transfer on three principal chromist groups at the heart of long-standing controversies. Our results provide robust support for acquisitions of photosynthesis through serial endosymbioses, beginning with the adoption of a red alga by cryptophytes, then a cryptophyte by the ancestor of ochrophytes, and finally an ochrophyte by the ancestor of haptophytes. Resolution of how chromist algae are related through endosymbioses provides a framework for unravelling the further reticulate history of red algal-derived plastids, and for clarifying evolutionary processes that gave rise to eukaryotic photosynthetic diversity.