The adjoint method is used to develop an objective analysis technique for estimating the vertical eddy viscosity used in three dimensional oceanic models. A cost functional which consists of two terms is formulated. The first term describes the difference, or lack of fit, between model results and available data. The second term measures the variance of the eddy viscosity with depth. Formulation of the cost functional is complete after coefficients (weights) are introduced to vary the relative influence of each of the terms. The ``optimized'' eddy viscosity estimate is obtained by minimizing the value of this functional. Results demonstrate the algorithm's ability to produce valid solutions to the posed problem. The smoothing term provides stability by limiting the change of the eddy viscosity in the vertical, and computer requirements are reduced with use of a ``Vertical Horizontal Splitting'' routine.