Sign language processing has traditionally relied on task-specific models, limiting the potential for transfer learning across tasks. Pre-training methods for sign language have typically focused on either supervised pre-training, which cannot take advantage of unlabeled data, or context-independent (frame or video segment) representations, which ignore the effects of relationships across time in sign language. We introduce SHuBERT (Sign Hidden-Unit BERT), a self-supervised contextual representation model learned from approximately 1,000 hours of American Sign Language video. SHuBERT adapts masked token prediction objectives to multi-stream visual sign language input, learning to predict multiple targets corresponding to clustered hand, face, and body pose streams. SHuBERT achieves state-of-the-art performance across multiple tasks including sign language translation, isolated sign language recognition, and fingerspelling detection.