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Given a terabyte click log, can we build an efficient and effective click model? It is commonly believed that web search click logs are a gold mine for search business, because they reflect users' preference over web documents presented by the search engine. Click models provide a principled approach to inferring user-perceived relevance of web documents, which can be leveraged in numerous applications in search businesses. Due to the huge volume of click data, scalability is a must.We present the click chain model (CCM), which is based on a solid, Bayesian framework. It is both scalable and incremental, perfectly meeting the computational challenges imposed by the voluminous click logs that constantly grow. We conduct an extensive experimental study on a data set containing 8.8 million query sessions obtained in July 2008 from a commercial search engine. CCM consistently outperforms two state-of-the-art competitors in a number of metrics, with over 9.7% better log-likelihood, over 6.2% better click perplexity and much more robust (up to 30%) prediction of the first and the last clicked position.