  We study the real time dynamics of $N_F$ flavors of fermions coupled to a
$U(1)$ gauge field in $2+1$ dimensions to leading order in a $1/N_F$ expansion.
For large enough $N_{F}$, this is an interacting conformal field theory and
describes the low energy properties of the Dirac spin liquid. We focus on
thermalization and the onset of many-body quantum chaos which can be diagnosed
from the growth of initally anti-commuting fermion field operators. We compute
such anti-commutators in this gauge theory to leading order in $1/N_F$. We find
that the anti-commutator grows exponentially in time and compute the quantum
Lyapunov exponent. We briefly comment on chaos, locality, and gauge invariance.
