Spelling correction is a particularly important problem in clinical natural language processing because of the abundant occurrence of misspellings in medical records. However, the scarcity of labeled datasets in a clinical context makes it hard to build a machine learning system for such clinical spelling correction. In this work, we present a probabilistic model of correcting misspellings based on a simple conditional independence assumption, which leads to a modular decomposition into a language model and a corruption model. With a deep character-level language model trained on a large clinical corpus, and a simple edit-based corruption model, we can build a spelling correction model with small or no real data. Experimental results show that our model significantly outperforms baselines on two healthcare spelling correction datasets.