Using the exact nonlinear equations of motion in the plane, an optimal guidance law for a vehicle pursuing a maneuvering evader is derived. It is assumed that a complete knowledge of the evader's motion is available to the pursuer. Both the pursuer and the evader move with constant velocities. The guidance law minimizes a weighted linear combination of the time of capture and the expended maneuvering energy. The equations of motion are solved in closed form in terms of elliptic integrals. Numerical results are presented in order to illustrate the advantages of the optimal guidance law as compared both with proportional navigation and a trajectory formed by a hard turn followed by a straight line. The extension of the approach to the three-dimensional case is also outlined.