Calculate the quantum Lyapunov exponent $\lambda_L$ and butterfly velocity $v_B$ in dilute Bose gas at the deep temperature $T$ of the Bose-Einstein condensed phase. A generalized Boltzmann equation approach is used to compute the out-of-time ordered correlator from which $\lambda_L$ and $v_B$ are extracted. At very low temperatures where elementary excitations are phonon-like, we find $\lambda_L\propto T^5$ and $v_B\sim c$, the speed of sound. At relatively high temperatures we have $\lambda_L\propto T$ and $v_B\sim c(T/T_*)^{0.23}$. We find that $\lambda_L$ is always comparable to the decay rate of a quasiparticle whose energy appropriately depends on $T$. On the other hand, the chaotic diffusion constant $D_L=v_B^2/\lambda_L$ is different from the energy diffusion constant $D_E$. $D_E\ll D_L$ at very low temperatures, $D_E\gg D_L$ otherwise.
