Syntactic parsing of web queries is important for query understanding. However, web queries usually do not observe the grammar of a written language, and no labeled syntactic trees for web queries are available. In this paper, we focus on a query's clicked sentence, i.e., a well-formed sentence that i) contains all the tokens of the query, and ii) appears in the query's top clicked web pages. We argue such sentences are semantically consistent with the query. We introduce algorithms to derive a query's syntactic structure from the dependency trees of its clicked sentences. This gives us a web query treebank without manual labeling. We then train a dependency parser on the treebank. Our model achieves much better UAS (0.86) and LAS (0.80) scores than state-of-the-art parsers on web queries.