The increasing availability of computing machines capable of parallel computation has accelerated interest in numerical methods that exhibit natural parallel structures. In particular, the parallel structure of the Picard method of successive approximations for the numerical solution of ordinary differential equations allows straightforward adaptation of the method for use on parallel computers. A matrix formulation of the Picard method for parallel computation is presented here in which the numerical solution is obtained in truncated Chebyshev series. The application of the formulation to parallel processing computing machines is discussed.