The discovery of frequent itemsets can serve valuable economic and research purposes. Releasing discovered frequent itemsets, however, presents privacy challenges. In this paper, we study the problem of how to perform frequent itemset mining on transaction databases while satisfying differential privacy. We propose an approach, called PrivBasis, which leverages a novel notion called basis sets. A theta-basis set has the property that any itemset with frequency higher than theta is a subset of some basis. We introduce algorithms for privately constructing a basis set and then using it to find the most frequent itemsets. Experiments show that our approach greatly outperforms the current state of the art.