  We predict synchronization of the chaotic dynamics of two atomic ensembles
coupled to a heavily damped optical cavity mode. The atoms are dissipated
collectively through this mode and pumped incoherently to achieve a macroscopic
population of the cavity photons. Even though the dynamics of each ensemble are
chaotic, their motions repeat one another. In our system, chaos first emerges
via quasiperiodicity and then synchronizes. We identify the signatures of
synchronized chaos, chaos, and quasiperiodicity in the experimentally
observable power spectra of the light emitted by the cavity.
