To date, the most widely used method for empirical analysis of multiple alternative qualitative choices has been an extension of binary logit analysis called conditional logit analysis. Although this method is extremely attractive because of its computational simplicity, it is burdened with a property termed the "independence of irrelevant alternatives" that is quite unrealistic in many choice situations. We have proposed in this paper a computationally feasible method of estimation not constrained by the independence restriction and which allows for a much richer range of human behavior than does the conditional logit model. An important characteristic of the model is provision for correlation among the random components of utility and, as a by-product, the explicit allowance for variation in tastes across individuals for the attributes of alternatives. We have demonstrated the model and compared it with the logit one by analyzing the travel mode choice decisions of commuters to the central business district of Washington, D.C. Substantial differences are found in predictions based on the two models. The example allows three alternatives. Extension to four or five is quite feasible.