Ciphertext-Policy Attribute-Based Encryption (CP-ABE) allows to encrypt data under an access policy, specified as a logical combination of attributes. Such ciphertexts can be decrypted by anyone with a set of attributes that fits the policy. In this paper, we introduce the concept of Distributed Attribute-Based Encryption (DABE), where an arbitrary number of parties can be present to maintain attributes and their corresponding secret keys. This is in stark contrast to the classic CP-ABE schemes, where all secret keys are distributed by one central trusted party. We provide the first construction of a DABE scheme; the construction is very efficient, as it requires only a constant number of pairing operations during encryption and decryption.