  We study domain growth properties of two species of particles executing
biased diffusion on a half-filled square lattice, consisting of just two lanes.
Driven in opposite directions by an external ``electric'' field, the particles
form clusters due to steric hindrance. While strictly one-dimensional systems
remain disordered, clusters in our ``quasi 1D'' case grow until only a single
macroscopic cluster survives. In the coarsening regime, the average cluster
size increases $\sim t^{0.6}$, significantly faster than in purely
diffusion-controlled systems. Remarkably, however, the cluster size
distribution displays dynamic scaling, following a form consistent with a
diffusion-limited growth mechanism.
