  We analytically study the Out-of-Time-Order Correlation functions (OTOC) for
two spatially separated primary operators in two-dimensional unitary minimal
models. Besides giving general arguments using the conformal symmetry, we also
use the Coulomb gas formalism to explicitly calculate the OTOC across the full
time regime. In contrast to large-$N$ chaotic systems, these models do not
display a separation of time scales, due to the lack of a large parameter. We
find that the physics at early times ($0<t-x\ll\beta$) and late times
($t-x\gg\beta$) are controlled by different OPE channels, which are related to
each other via the braiding matrix. The normalized OTOC obeys a power-law decay
with a fractional power at early times and approaches a generically nonzero
value in an exponential way at late times. The late time value is related to
the modular $S$-matrix and is in agreement with earlier calculations. All of
the results above are readily generalized to rational conformal field theories.
