  We study the generalization of the Sachdev-Ye-Kitaev (SYK) model to a $1+1$
dimensional chiral SYK model of $N$ flavors of right-moving chiral Majorana
fermions with all-to-all random 4-fermion interactions. The interactions in
this model are exactly marginal, leading to an exact scaling symmetry. We show
the Schwinger-Dyson equation of this model in the large $N$ limit is exactly
solvable. In addition, we show this model is integrable for small $N\le6$ by
bosonization. Surprisingly, the two point function in the large $N$ limit has
exactly the same form as that for $N=4$, although the four point functions of
the two cases are quite different. The ground state entropy in the large $N$
limit is the same as that of $N$ free chiral Majorana fermions, leading to a
zero ground state entropy density. The OTOC of the model in the large $N$ limit
exhibits a non-trivial spacetime structure reminscent of that found by Gu and
Kitaev for generic SYK-like models. Specifically we find a Lyapunov regime
inside an asymmetric butterfly cone, which are signatures of quantum chaos, and
that the maximal velocity dependent Lyapunov exponent approaches the chaos
bound $2\pi/\beta$ as the interaction strength approaches its physical upper
bound. Finally, the model is integrable for (at least) $N\le6$ but chaotic in
the large $N$ limit, leading us to conjecture that there is a transition from
integrability to chaos as $N$ increases past a critical value.
