Is it reasonable to teach the ideas and methods of Bayesian inference in a first statistics course for general students? This paper argues that it is, at best, premature to do so. Surveys of the statistical methods actually in use suggest that Bayesian techniques are little used. Moreover, Bayesians have not yet agreed on standard approaches to standard problem settings. Bayesian reasoning requires a grasp of conditional probability, a concept confusing to beginners. Finally, an emphasis on Bayesian inference might well impede the trend toward experience with real data and a better balance among data analysis, data production, and inference in first statistics courses