Circadian rhythms are common in eukaryotes, but the several claimed cases in prokaryotes are all open to alternative interpretation. We report here a clearcut circadian rhythm in cell division in a marine Synechococcus sp. strain WH7803, under conditions where the generation time is longer than one day, that is entrained by a light–dark cycle, and that persists for at least four cycles in continuous light (2 μE·m−2·s−1) and constant temperature (22, 20 or 16°C) with a maximum in dividing cells at about 24 h intervals. Thus, the prokaryote, Synechococcus, satisfies the criteria for the possession of a true temperature-compensated circadian clock. Were the existence of such a rhythm confirmed, current hypotheses that intracellular compartments are required for circadian timing may require modification.