Generating user interpretable multi-class predictions in data-rich environments with many classes and explanatory covariates is a daunting task. We introduce Diagonal Orthant Latent Dirichlet Allocation (DOLDA), a supervised topic model for multi-class classification that can handle many classes as well as many covariates. To handle many classes we use the recently proposed Diagonal Orthant probit model (Johndrow et al., in: Proceedings of the sixteenth international conference on artificial intelligence and statistics, 2013) together with an efficient Horseshoe prior for variable selection/shrinkage (Carvalho et al. in Biometrika 97:465-480, 2010). We propose a computationally efficient parallel Gibbs sampler for the new model. An important advantage of DOLDAis that learned topics are directly connected to individual classes without the need for a reference class. We evaluate the model's predictive accuracy and scalability, and demonstrate DOLDA's advantage in interpreting the generated predictions.