Many-body systems which saturate the quantum bound on chaos are attracting interest across a wide range of fields. Notable examples include the Sachdev-Ye-Kitaev model and its variations, all characterised by some form or randomness and all to all couplings. Here we study many-body quantum chaos in a quantum impurity model showing Non-Fermi-Liquid physics, the overscreened multichannel $SU(N)$ Kondo model. We compute exactly the low-temperature behavior of the out-of time order correlator in the limit of large $N$ and large number of channels $K$, at fixed ratio $\gamma=K/N$. Due to strong correlations at the impurity site the spin fractionalizes in auxiliary fermions and bosons. We show that all the degrees of freedom of our theory acquire a Lyapunov exponent which is linear in temperature as $T\rightarrow 0$, with a prefactor that depends on $\gamma$. Remarkably, for $N=K$ the impurity spin displays maximal chaos, while bosons and fermions only get up to half of the maximal Lyapunov exponent. Our results highlights two new features: a non-disordered model which is maximally chaotic due to strong correlations at its boundary and a fractionalization of quantum chaos.