We consider a two-state tracking problem with bearing measurements on a stationary target. The observer’s speed is assumed constant and an optimum course is sought. An integral representing a lower bound for the Fisher information matrix is derived, and optimality of the observer’s course is defined as maximizing the lower bound. The problem is solved within the framework of optimal control theory. A sufficiency theorem involving the Hamilton-Jacobi equation is invoked to determine the optimal course. It is shown that the optimal course is such that the observer proceeds at a fixed deviated angle and the optimal trajectory is a deviated pursuit curve.