Recent work on unsupervised question answering has shown that models can be trained with procedurally generated question-answer pairs and can achieve performance competitive with supervised methods. In this work, we consider the task of unsupervised reading comprehension and present a method that performs "test-time learning" (TTL) on a given context (text passage), without requiring training on large-scale human-authored datasets containing \textit{context-question-answer} triplets. This method operates directly on a single test context, uses self-supervision to train models on synthetically generated question-answer pairs, and then infers answers to unseen human-authored questions for this context. Our method achieves accuracies competitive with fully supervised methods and significantly outperforms current unsupervised methods. TTL methods with a smaller model are also competitive with the current state-of-the-art in unsupervised reading comprehension.