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Serverless computing is a new pay-per-use cloud service paradigm that automates resource scaling for stateless functions and can potentially facilitate bursty machine learning serving. Batching is critical for latency performance and cost-effectiveness of machine learning inference, but unfortunately it is not supported by existing serverless platforms due to their stateless design. Our experiments show that without batching, machine learning serving cannot reap the benefits of serverless computing. In this paper, we present BATCH, a framework for supporting efficient machine learning serving on serverless platforms. BATCH uses an optimizer to provide inference tail latency guarantees and cost optimization and to enable adaptive batching support. We prototype BATCH atop of AWS Lambda and popular machine learning inference systems. The evaluation verifies the accuracy of the analytic optimizer and demonstrates performance and cost advantages over the state-of-the-art method MArk and the state-of-the-practice tool SageMaker.