We initiate a study of on-line ciphers. These are ciphers that can take input plaintexts of large and varying lengths and will output the ith block of the ciphertext after having processed only the first i blocks of the plaintext. Such ciphers permit length-preserving encryption of a data stream with only a single pass through the data. We provide security definitions for this primitive and study its basic properties. We then provide attacks on some possible candidates, including CBC with fixed IV. Finally we provide a construction called HCBC which is based on a given block cipher E and a family of AXU functions. HCBC is proven secure against chosen-plaintext attacks assuming that E is a PRP secure against chosen-plaintext attacks