  We reveal a continuous dynamical heating transition between a prethermal and
an infinite-temperature stage in a clean, chaotic periodically driven classical
spin chain. The transition time is a steep exponential function of the drive
frequency, showing that the exponentially long-lived prethermal plateau,
originally observed in quantum Floquet systems, survives the classical limit.
Even though there is no straightforward generalization of Floquet's theorem to
nonlinear systems, we present strong evidence that the prethermal physics is
well described by the inverse-frequency expansion. We relate the stability and
robustness of the prethermal plateau to drive-induced synchronization not
captured by the expansion. Our results set the pathway to transfer the ideas of
Floquet engineering to classical many-body systems, and are directly relevant
for photonic crystals and cold atom experiments in the superfluid regime.
