  We construct and study a chiral Sachdev-Ye (SY) model consisting of $N$
chiral SU$(M)_1$ Wess-Zumino-Witten (WZW) models with current-current
interactions among each other, which generalizes the 0+1d quantum chaotic SY
spin model into 1+1d chiral system with anyon excitations. Each WZW model hosts
Abelian anyons as charge excitations, and may arise as the chiral edge theory
of 2+1d gapped topological phases. We solve the chiral SY model in two limits
which show distinct quantum dynamics. The first limit is the case with uniform
interactions at any integers $N$ and $M$, which is integrable and decomposes
into a chiral SU$(M)_N$ WZW model and its coset with different "speed of
light". When $N=M=2$, the model maps to a free Majorana fermion model. The
second limit is the large $N$ and $M$ limit with random interactions, which is
solvable to the leading $\frac{1}{NM}$ order, and exhibits many-body quantum
chaos in the out-of-time-ordered correlation of anyons. As the interaction
strength approaches the upper limit preserving the chirality, the leading
velocity-dependent Lyapunov exponent of the model saturates the maximal chaos
bound $2\pi/\beta$ at temperature $\beta^{-1}$.
