The minimum logit chi-squared estimator, as originally proposed by Berkson (1944, 1955), has been suggested for use in estimating the parameters in a linear logistic regression model for binomial response data. It is asymptotically normal when the number of design points goes to infinity under some mild restrictions on the distribution of observations over design points, as shown by Davis (1985). In this paper, a generalization of the minimum logit chi-squared estimator is introduced in order to extend its scope to a family of asymmetric probability models proposed by Prentice (1976b). We also show that the generalized minimum logit chi-squared estimator is asymptotically chi-square in distribution.