Missing values are endemic in the data sets available to econometricians. This paper suggests a semiparametrically efficient likelihood-based approach to deal with general non-ignorable missing data problems for discrete choice models. Our concern is when the dependent variable and/or covariates are unobserved for some sampling units. A supplementary random sample of observations on all covariates may be available. The key insight of this paper is the recognition of non-response as a modification of choice-based (CB) samples. Semiparametrically efficient generalized method of moments (GMM) estimation appropriate for CB samples is then adapted for the non-response framework considered in this paper. Simulation results for various GMM estimators proposed here are very encouraging.