The length scale of the local chemical anisotropy responsible for the growth-temperature-induced perpendicular magnetic anisotropy of face-centered cubic CoPt(3) alloy films was investigated using polarized extended x-ray absorption fine structure (EXAFS). These x-ray measurements were performed on a series of four (111) CoPt(3) films epitaxially grown on (0001) sapphire substrates. The EXAFS data show a preference for Co-Co pairs parallel to the film plane when the film exhibits magnetic anisotropy, and random chemical order otherwise. Furthermore, atomic pair correlation anisotropy was evidenced only in the EXAFS signal from the next neighbors to the absorbing Co atoms and from multiple scattering paths focused through the next neighbors. This suggests that the Co clusters are no more than a few atoms in extent in the plane and one monolayer in extent out of the plane. Our EXAFS results confirm the correlation between perpendicular magnetic anisotropy and two-dimensional Co segregation in CoPt(3) alloy films, and establish a length scale on the order of 10 Å for the Co clusters.