All adult flatfishes (Pleuronectiformes), including the gastronomically familiar plaice, sole, turbot and halibut, have highly asymmetrical skulls, with both eyes placed on one side of the head. This arrangement, one of the most extraordinary anatomical specializations among vertebrates, arises through migration of one eye during late larval development. Although the transformation of symmetrical larvae into asymmetrical juveniles is well documented, the evolutionary origins of flatfish asymmetry are uncertain because there are no transitional forms linking flatfishes with their symmetrical relatives. The supposed inviability of such intermediates gave pleuronectiforms a prominent role in evolutionary debates, leading to attacks on natural selection and arguments for saltatory change. Here I show that Amphistium and the new genus Heteronectes, both extinct spiny-finned fishes from the Eocene epoch of Europe, are the most primitive pleuronectiforms known. The orbital region of the skull in both taxa is strongly asymmetrical, as in living flatfishes, but these genera retain many primitive characters unknown in extant forms. Most remarkably, orbital migration was incomplete in Amphistium and Heteronectes, with eyes remaining on opposite sides of the head in post-metamorphic individuals. This condition is intermediate between that in living pleuronectiforms and the arrangement found in other fishes. Amphistium and Heteronectes indicate that the evolution of the profound cranial asymmetry of extant flatfishes was gradual in nature.