We introduce a novel topic modeling approach based on constructing a semantic set cover for clusters of similar documents. Specifically, our approach first clusters documents using their Tf-Idf representation, and then covers each cluster with a set of topic words based on semantic similarity, defined in terms of a word embedding. Computing a topic cover amounts to solving a minimum set cover problem. Our evaluation compares our topic modeling approach to Latent Dirichlet Allocation (LDA) on three metrics: 1) qualitative topic match, measured using evaluations by Amazon Mechanical Turk (MTurk) workers, 2) performance on classification tasks using each topic model as a sparse feature representation, and 3) topic coherence. We find that qualitative judgments significantly favor our approach, the method outperforms LDA on topic coherence, and is comparable to LDA on document classification tasks.