Suppose a client, Alice, has outsourced her data to an external storage provider, Bob, because he has capacity for her massive data set, of size n, whereas her private storage is much smaller--say, of size O(n^{1/r}), for some constant r > 1. Alice trusts Bob to maintain her data, but she would like to keep its contents private. She can encrypt her data, of course, but she also wishes to keep her access patterns hidden from Bob as well. We describe schemes for the oblivious RAM simulation problem with a small logarithmic or polylogarithmic amortized increase in access times, with a very high probability of success, while keeping the external storage to be of size O(n). To achieve this, our algorithmic contributions include a parallel MapReduce cuckoo-hashing algorithm and an external-memory dataoblivious sorting algorithm.