Synchronization, the temporal coordination of coupled oscillators, allows fireflies to flash in unison, neurons to fire collectively, and human crowds to fall in step on the London millenium bridge. Here, we interpret active (or self-propelled) chiral microswimmers with a distribution of intrinsic frequencies as motile oscillators and show that they can synchronize over very large distances, even for local coupling in two dimensions (2D). This opposes canonical nonactive oscillators on static or time-dependent networks, leading to synchronized domains only. A consequence of this activity-induced synchronization is the emergence of a 'mutual flocking phase,' where particles of opposite chirality cooperate to form superimposed flocks moving at a relative angle to each other, providing a chiral active matter analogue to the celebrated Toner-Tu phase. The underlying mechanism employs a positive feedback loop involving the two-way coupling between oscillators' phase and self-propulsion and could be exploited as a design principle for synthetic active materials and chiral self-sorting techniques.