Ocean-bottom seismometers (OBSs) are equipped with seismic sensors that record acoustic and seismic events at the seafloor, which makes them suitable for investigating tectonic structures capable of generating earthquakes offshore. One critical parameter to obtain accurate earthquake locations is the absolute time of the incoming seismic signals recorded by the OBSs. It is, however, not possible to synchronize the internal clocks of the OBSs with a known reference time, given that GNSS signals are unable to reach the instrument at the sea bottom. To address this issue, here we introduce a new method to synchronize the clocks of large-scale OBS deployments. Our approach relies on the theoretical time-symmetry of time-lapse (averaged) crosscorrelations of ambient seismic noise. Deviations from symmetry are attributed to clock errors. This implies that the recovered clock errors will be obscured by lapse crosscorrelations' deviations from symmetry that are not due to clock errors. Non-uniform surface wave illumination patterns are arguably the most notable source which breaks the time symmetry. Using field data, we demonstrate that the adverse effects of non-uniform illumination patterns on the recovered clock errors can be mitigated by means of a weighted least-squares inversion that is based on station-station distances. In addition, our methodology permits the recovery of timing errors at the time of deployment of the OBSs. This error can be attributed to either: i) a wrong initial time synchronization of the OBS or ii) a timing error induced by changing temperature and pressure conditions while the OBS is sunk to the ocean floor. The methodology is implemented in an open-source Python package named OCloC, and we applied it to the OBS recordings acquired in the context of the IMAGE project in and around Reykjanes, Iceland. As expected, most OBSs suffered from clock drift. Surprisingly, we found incurred timing errors at the time of deployment for most of the OBSs.