  We study the first non-planar correction to gluon scattering amplitudes in
${\cal N}=4$ SYM theory. The correction takes the form of a double trace
partial amplitude and is suppressed by one power of $1/N$ with respect to the
leading single trace contribution. We extend the duality between planar
scattering amplitudes and null polygonal Wilson loops to the double trace
amplitude. The new duality relates the amplitude to the correlation function of
two infinite null polygonal Wilson lines that are subject to a quantum
periodicity constraint. We test the duality perturbatively at one-loop order
and demonstrate it for the dual string in AdS. The duality allows us to extend
the notion of the loop integrand beyond the planar limit and to determine it
using recursion relations. It also allows one to apply the integrability-based
pentagon operator product expansion approach to the first non-planar order.
