  We derive a quantiative propagation of chaos result for a mixed-sign point
vortex system on $\mathbb{T}^2$ with independent Brownian noise, at an optimal
rate. We introduce a pairing between vortices of opposite sign, and using the
vorticity formulation of 2D Navier-Stokes, we define an associated tensorized
vorticity equation on $\mathbb{T}^2\times\mathbb{T}^2$ with the same
well-posedness theory as the original equation. Solutions of the new PDE can be
projected onto solutions of Navier-Stokes, and the tensorized equation allows
us to exploit existing propagation of chaos theory for identical particles.
