Significance The suprachiasmatic nucleus (SCN) is the principal circadian clock of the mammalian brain. To function effectively, SCN neurons must operate as a synchronized circuit. How cell-autonomous and circuit-level circadian mechanisms interact to achieve this is unclear. Here, we used intersectional genetics to create temporally chimeric mice where both 24-h and 20-h clock neurons were present in the SCN, in different cell populations. The 24-h dopamine receptor-positive cells set the speed of the SCN, imposing their cell-autonomous 24-h period on all cells in the circuit. Exposure to a 20-h lighting cycle, however, inverted this dominance, reprograming the circuit to 20 h. These results show how robust circuit-level signaling underlies complex, nonlinear computations of circadian period that also exhibit a remarkable level of plasticity.