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Collaborative filtering is a widely-used technique in online services to enhance the accuracy of a recommender system. This technique, however, comes at the cost of users having to reveal their preferences, which has undesirable privacy implications. We propose a collaborative filtering system where the system does not observe the users' data and is still able to provide useful recommendations. Compared to prior systems, our emphasis is on building a practical system that can be reasonably used by a large number of users. Our approach involves creating a primitive to cluster similar users privately by modifying existing methods such as Locality Sensitive Hashing. Another technique we use is artificial ratings, as part of the process of privately predicting the rating for an item within a particular cluster. We evaluate our scheme on the Netflix Prize dataset, reporting the accuracy of our recommendations as a function of the privacy provided.