Lexical substitutes have found use in areas such as paraphrasing, text simplification, machine translation, word sense disambiguation, and part of speech induction. However the computational complexity of accurately identifying the most likely substitutes for a word has made large scale experiments difficult. In this letter we introduce a new search algorithm, FASTSUBS, that is guaranteed to find the K most likely lexical substitutes for a given word in a sentence based on an n-gram language model. The computation is sublinear in both K and the vocabulary size V. An implementation of the algorithm and a dataset with the top 100 substitutes of each token in the WSJ section of the Penn Treebank are available at http://goo.gl/jzKH0.