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We define the novel problem of extracting and predicting occurrence dates for a class of recurrent events -- events that are held periodically as per a near-regular schedule (e.g., conferences, film festivals, sport championships). Knowledge-bases such as Freebase contain a large number of such recurring events, but they also miss substantial information regarding specific event instances and their occurrence dates. We develop a temporal extraction and inference engine to fill in the missing dates as well as to predict their future occurrences. Our engine performs joint inference over several knowledge sources -- (1) information about an event instance and its date extracted from text by our temporal extractor, (2) information about the typical schedule (e.g., ``every second week of June") for a recurrent event extracted by our schedule extractor, and (3) known dates for other instances of the same event. The output of our system is a representation for the event schedule and an occurrence date for each event instance. We find that our system beats humans in predicting future occurrences of recurrent events by significant margins. We release our code and system output for further research.