The survival of organisms depends on their ability to adapt to their environment, one important aspect of which is the daily cycle of day and night. During the day, organisms use a variety of strategies to protect themselves from deleterious ultraviolet (UV) wavelengths of sunlight. Among those strategies could be timing of UV-sensitive cellular processes to occur at night to avoid UV-induced damage. We tested whether the unicellular alga Chlamydomonas reinhardtii uses this strategy by measuring the survival of cells following exposure to UV radiation at different phases of the day. Chlamydomonas cells displayed a rhythm of survival from UV radiation where the most sensitive phases occurred during the end of the day and at the beginning of the night. This phase of sensitivity corresponds to the time of nuclear division. The rhythm continues in constant light indicating control by a circadian clock. The results presented here suggest a hypothesis of how circadian clocks may have evolved; a temporal program whereby light-sensitive processes are timed to avoid sunlight-induced damage would be advantageous and therefore selected.