The Co-Pt nanochessboard is a quasi-periodic, nanocomposite tiling of L10 and L12 magnetic phases that offers a novel structure for the investigation of exchange coupling, relevant to permanent magnet applications. Periodicity of the tiling is controlled by the rate of cooling through the eutectoid isotherm, resulting in control over the L10-L12 exchange coupling. First order reversal curve analysis reveals a transition from partial coupling to nearly complete exchange-coupling in a Co40.2Pt59.8 nanochessboard structured alloy as the periodicity is reduced below the critical correlation length. Micromagnetic simulations give insights into how exchange coupling manifests in the tiling, and its impact on microscopic magnetization reversal mechanisms.