In this paper, the continuous Galerkin Petrov time discretization (cGP) scheme is applied to the Chen system, which is a three-dimensional system of ordinary differential equations (ODEs) with quadratic nonlinearities. In particular, we implement and analyze numerically the higher order cGP(2)-method which is found to be of fourth order at the discrete time points. A numerical comparison with classical fourth-order Runge–Kutta (RK4) is given for the presented problem. We look at the accuracy of the cGP(2) as the Chen system changes from a nonchaotic system to a chaotic one. It is shown that the cGP(2) method gains accurate results at larger time step sizes for both cases.