This paper introduces Chart Inference (CI), an algorithm for deriving a CCG category for an unknown word from a partial parse chart. It is shown to be faster and more precise than a baseline brute-force method, and to achieve wider coverage than a rule-based system. In addition, we show the application of CI to a domain adaptation task for question words, which are largely missing in the Penn Treebank. When used in combination with self-training, CI increases the precision of the baseline StatCCG parser over subjectextraction questions by 50%. An error analysis shows that CI contributes to the increase by expanding the number of category types available to the parser, while self-training adjusts the counts. 1