Many organisms possess internal biochemical clocks, known as circadian oscillators, which allow them to regulate their biological activity with a 24-hour period. It was recently discovered that the circadian oscillator of photosynthetic cyanobacteria is able to function in a test tube with only three proteins, KaiA, KaiB, and KaiC, and ATP. Biochemical events are intrinsically stochastic, and this tends to desynchronize oscillating protein populations. We propose that stability of the Kai-protein oscillator relies on active synchronization by (i) monomer exchange between KaiC hexamers during the day, and (ii) formation of clusters of KaiC hexamers at night. Our results highlight the importance of collective assembly or disassembly of proteins in biochemical networks, and may help guide design of novel protein-based oscillators.