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Many organizations wish to collaboratively train machine learning models on their combined datasets for a common benefit (e.g., better medical research, or fraud detection). However, they often cannot share their plaintext datasets due to privacy concerns and/or business competition. In this paper, we design and build Helen, a system that allows multiple parties to train a linear model without revealing their data, a setting we call coopetitive learning. Compared to prior secure training systems, Helen protects against a much stronger adversary who is malicious and can compromise m−1 out of m parties. Our evaluation shows that Helen can achieve up to five orders of magnitude of performance improvement when compared to training using an existing state-of-the-art secure multi-party computation framework.