Until recently, intricate details of the optical design of non-biomineralized arthropod eyes remained elusive in Cambrian Burgess-Shale-type deposits, despite exceptional preservation of soft-part anatomy in such Konservat-Lagerstätten. The structure and development of ommatidia in arthropod compound eyes support a single origin some time before the latest common ancestor of crown-group arthropods, but the appearance of compound eyes in the arthropod stem group has been poorly constrained in the absence of adequate fossils. Here we report 2-3-cm paired eyes from the early Cambrian (approximately 515 million years old) Emu Bay Shale of South Australia, assigned to the Cambrian apex predator Anomalocaris. Their preserved visual surfaces are composed of at least 16,000 hexagonally packed ommatidial lenses (in a single eye), rivalling the most acute compound eyes in modern arthropods. The specimens show two distinct taphonomic modes, preserved as iron oxide (after pyrite) and calcium phosphate, demonstrating that disparate styles of early diagenetic mineralization can replicate the same type of extracellular tissue (that is, cuticle) within a single Burgess-Shale-type deposit. These fossils also provide compelling evidence for the arthropod affinities of anomalocaridids, push the origin of compound eyes deeper down the arthropod stem lineage, and indicate that the compound eye evolved before such features as a hardened exoskeleton. The inferred acuity of the anomalocaridid eye is consistent with other evidence that these animals were highly mobile visual predators in the water column. The existence of large, macrophagous nektonic predators possessing sharp vision--such as Anomalocaris--within the early Cambrian ecosystem probably helped to accelerate the escalatory 'arms race' that began over half a billion years ago.