In catalytic methanol oxidation on ultrathin vanadium oxide layers on Rh(111) (Θ_{V}≈0.2 monolayer equivalent) we observe a 2D ripening of the VO_{x} islands that is controlled by the catalytic reaction. Neighboring VO_{x} islands move under reaction conditions towards each other and coalesce. The motion and the coalescence of the islands are explained by a polymerization-depolymerization equilibrium that is sensitive to gradients in the adsorbate coverages.