  We compute Out-of-Time-Order correlators (OTOCs) for conformal field theories
(CFTs) subjected to either continuous or discrete periodic drive protocols.
This is achieved by an appropriate analytic continuation of the stroboscopic
time. After detailing the general structure, we perform explicit calculations
in large-$c$ CFTs where we find that OTOCs display an exponential, an
oscillatory and a power-law behaviour in the heating phase, the non-heating
phase and on the phase boundary, respectively. In contrast to this, for the
Ising CFT representing an integrable model, OTOCs never display such
exponential growth. This observation hints towards how OTOCs can demarcate
between integrable and chaotic CFT models subjected to a periodic drive. We
further explore properties of the light-cone which is characterized by the
corresponding butterfly velocity as well as the Lyapunov exponent.
Interestingly, as a consequence of the spatial inhomogeneity introduced by the
drive, the butterfly velocity, in these systems, has an explicit dependence on
the initial location of the operators. We chart out the dependence of the
Lyapunov exponent and the butterfly velocities on the frequency and amplitude
of the drive for both protocols and discuss the fixed point structure which
differentiates such driven CFTs from their un-driven counterparts.
