We develop a parameter estimation routine for multinomial logit discrete choice models in which one alternative is completely censored, i.e., when one alternative is never observed to have been chosen in the estimation data set. Our method is based on decomposing the log-likelihood function into marginal and conditional components. Our method is computationally efficient, provides consistent parameter estimates, and can easily incorporate price and other product attributes. Simulations based on industry hotel data demonstrate the superior computational performance of our method over alternative estimation methods that are capable of estimating price effects. Because most existing revenue management choice-based optimization algorithms do not include price as a decision variable, our estimation procedure provides the inputs needed for more advanced product portfolio availability and price optimization models.