Multicellularity is often considered a prerequisite for morphological complexity, as seen in the camera-type eyes found in several groups of animals. A notable exception exists in single-celled eukaryotes called dinoflagellates, some of which have an eye-like 'ocelloid' consisting of subcellular analogues to a cornea, lens, iris, and retina. These planktonic cells are uncultivated and rarely encountered in environmental samples, obscuring the function and evolutionary origin of the ocelloid. Here we show, using a combination of electron microscopy, tomography, isolated-organelle genomics, and single-cell genomics, that ocelloids are built from pre-existing organelles, including a cornea-like layer made of mitochondria and a retinal body made of anastomosing plastids. We find that the retinal body forms the central core of a network of peridinin-type plastids, which in dinoflagellates and their relatives originated through an ancient endosymbiosis with a red alga. As such, the ocelloid is a chimaeric structure, incorporating organelles with different endosymbiotic histories. The anatomical complexity of single-celled organisms may be limited by the components available for differentiation, but the ocelloid shows that pre-existing organelles can be assembled into a structure so complex that it was initially mistaken for a multicellular eye. Although mitochondria and plastids are acknowledged chiefly for their metabolic roles, they can also be building blocks for greater structural complexity.