An extension of the Bock-Samejima model for multiple choice items is introduced. The model provides for varying probabilities of the response alternative when the examinee guesses. A marginal maximum likelihood method is devised for estimating the item parameters, and likelihood ratio tests for comparing more and less constrained forms of the model are provided. Applications of the model are illustrated with item response data for the word knowledge and general science subtests of the Armed Services Vocational Aptitude Battery. (Author)