A theory of correlated many chain motions is developed for linear chain polymer melts. The center of mass diffusion constant of the chains is shown to be inversely proportional to the number of monomers that have their motion correlated with the motion of any given monomer. This quantity is expressed as the integral over the normalized correlation function for the displacements of different monomers in the melt. Two limiting cases are considered for this correlation function in monodisperse melts. The loss of correlation in the motion of monomers occurs because of the relative motion of the chains. The first limiting case assumes that the relative chain motions are correlated over the entire range of the correlated many chain motion. This case leads to the largest single contribution to the diffusion constant in the long chain limit. The second limiting case employs the shortest possible correlation length for the relative displacements of the chains. Since this case allows for the greatest randomness in the motion of the chains, it is expected that the contribution from this type of correlated motion should dominate the chain diffusion constant. The diffusion constant based on the correlated motions in the melt is consistent with the experimentally observed chain length scaling of both the terminal time and the chain diffusion constant. The case of the diffusion of a single probe chain in a melt of host chains of different length is also discussed.