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We present an approach for generating clarification questions with the goal of eliciting new information that would make the given textual context more complete. We propose that modeling hypothetical answers (to clarification questions) as latent variables can guide our approach into generating more useful clarification questions. We develop a Generative Adversarial Network (GAN) where the generator is a sequence-to-sequence model and the discriminator is a utility function that models the value of updating the context with the answer to the clarification question. We evaluate on two datasets, using both automatic metrics and human judgments of usefulness, specificity and relevance, showing that our approach outperforms both a retrieval-based model and ablations that exclude the utility model and the adversarial training.