  We calculate the quantum Lyapunov exponent $\lambda_L$ and butterfly velocity
$v_B$ in the dilute Bose gas at temperature $T$ deep in the Bose-Einstein
condensation phase. The generalized Boltzmann equation approach is used for
calculating out-of-time ordered correlators, from which $\lambda_L$ and $v_B$
are extracted. At very low temperature where elementary excitations are
phonon-like, we find $\lambda_L\propto T^5$ and $v_B\sim c$, the sound
velocity. At relatively high temperature, we have $\lambda_L\propto T$ and
$v_B\sim c(T/T_*)^{0.23}$. We find $\lambda_L$ is always comparable to the
damping rate of a quasiparticle, whose energy depends suitably on $T$. The
chaos diffusion constant $D_L=v_B^2/\lambda_L$, on the other hand, differs from
the energy diffusion constant $D_E$. We find $D_E\ll D_L$ at very low
temperature and $D_E\gg D_L$ otherwise.
