  We propose an extension of the Sachdev-Ye-Kitaev (SYK) model that exhibits a
quantum phase transition from the previously identified non-Fermi liquid fixed
point to a Fermi liquid like state, while still allowing an exact solution in a
suitable large $N$ limit. The extended model involves coupling the interacting
$N$-site SYK model to a new set of $pN$ peripheral sites with only quadratic
hopping terms between them. The conformal fixed point of the SYK model remains
a stable low energy phase below a critical ratio of peripheral sites $p<p_c(n)$
that depends on the fermion filling $n$. The scrambling dynamics throughout the
non-Fermi liquid phase is characterized by a universal Lyapunov exponent
$\lambda_L\to 2\pi T$ in the low temperature limit, however the temperature
scale marking the crossover to the conformal regime vanishes continuously at
the critical point $p_c$. The residual entropy at $T\to 0$, non zero in the
NFL, also vanishes continuously at the critical point. For $p>p_c$ the
quadratic sites effectively screen the SYK dynamics, leading to a quadratic
fixed point in the low temperature and frequency limit. The interactions have a
perturbative effect in this regime leading to scrambling with Lyapunov exponent
$\lambda_L\propto T^2$.
