A procedure for designing an optimal observer for a linear continuous time invariant system is described in this paper. The parameters of the observer are chosen so as to assign its eigenvalues to desired locations and at the same time a measure of the deviation of the estimate of the observed state from its actual value is minimized, A numerical example is included to show that the estimate of the state obtained by the optimal observer is much closer to the actual state than the estimate obtained from another observer with the same eigenvalues as the optimal observer.