Mating between different species produces hybrids that are usually asexual and stuck as diploids, but can also lead to the formation of new species. Here, we report the genome sequences of 27 isolates of the pathogenic yeast Candida orthopsilosis. We find that most isolates are diploid hybrids, products of mating between two unknown parental species (A and B) that are 5% divergent in sequence. Isolates vary greatly in the extent of homogenization between A and B, making their genomes a mosaic of highly heterozygous regions interspersed with homozygous regions. Separate phylogenetic analyses of SNPs in the A- and B-derived portions of the genome produces almost identical trees of the isolates with four major clades. However, the presence of two mutually exclusive genotype combinations at the mating type locus, and recombinant mitochondrial genomes diagnostic of inter-clade mating, shows that the species C. orthopsilosis does not have a single evolutionary origin but was created at least four times by separate interspecies hybridizations between parents A and B. Older hybrids have lost more heterozygosity. We also identify two isolates with homozygous genomes derived exclusively from parent A, which are pure non-hybrid strains. The parallel emergence of the same hybrid species from multiple independent hybridization events is common in plant evolution, but is much less documented in pathogenic fungi.