We present SwellShark, a framework for building biomedical named entity recognition (NER) systems quickly and without hand-labeled data. Our approach views biomedical resources like lexicons as function primitives for autogenerating weak supervision. We then use a generative model to unify and denoise this supervision and construct large-scale, probabilistically labeled datasets for training high-accuracy NER taggers. In three biomedical NER tasks, SwellShark achieves competitive scores with state-of-the-art supervised benchmarks using no hand-labeled training data. In a drug name extraction task using patient medical records, one domain expert using SwellShark achieved within 5.1% of a crowdsourced annotation approach – which originally utilized 20 teams over the course of several weeks – in 24 hours.