Competition between parasite species or genotypes can play an important role in the establishment of parasites in new host populations. Here, we investigate a mechanism by which a rare parasite is unable to establish itself in a host population if a common resident parasite is already present (a ‘priority effect’). We develop a simple epidemiological model and show that a rare parasite genotype is unable to invade if coinfecting parasite genotypes inhibit each other's transmission more than expected from simple resource partitioning. This is because a rare parasite is more likely to be in multiply-infected hosts than the common genotype, and hence more likely to pay the cost of reduced transmission. Experiments competing interfering clones of bacteriophage infecting a bacterium support the model prediction that the clones are unable to invade each other from rare. We briefly discuss the implications of these results for host-parasite ecology and (co)evolution.