  We compute the $O(1/N^3)$ correction to the critical exponent $\eta$ in the
chiral XY or chiral Gross-Neveu model in $d$-dimensions. As the leading order
vertex anomalous dimension vanishes, the direct application of the large $N$
conformal bootstrap formalism is not immediately possible. To circumvent this
we consider the more general Nambu-Jona-Lasinio model for a general non-abelian
Lie group. Taking the abelian limit of the exponents of this model produces
those of the chiral XY model. Subsequently we provide improved estimates for
$\eta$ in the three dimensional chiral XY model for various values of $N$.
