Near-duplicate video retrieval (NDVR) has been a significant research task in multimedia given its high impact in applications, such as video search, recommendation, and copyright protection. In addition to accurate retrieval performance, the exponential growth of online videos has imposed heavy demands on the efficiency and scalability of the existing systems. Aiming at improving both the retrieval accuracy and speed, we propose a novel stochastic multiview hashing algorithm to facilitate the construction of a large-scale NDVR system. Reliable mapping functions, which convert multiple types of keyframe features, enhanced by auxiliary information such as video-keyframe association and ground truth relevance to binary hash code strings, are learned by maximizing a mixture of the generalized retrieval precision and recall scores. A composite Kullback-Leibler divergence measure is used to approximate the retrieval scores, which aligns stochastically the neighborhood structures between the original feature and the relaxed hash code spaces. The efficiency and effectiveness of the proposed method are examined using two public near-duplicate video collections and are compared against various classical and state-of-the-art NDVR systems.