Humane and Existing Alternatives in Research and Testing Sciences Act of 2019 or the HEARTS Act of 2019 This bill directs the National Institutes of Health (NIH) to promote nonanimal research methods. Specifically, NIH must (1) provide incentives for nonanimal research and (2) require the evaluation of viable nonanimal methods before approving animal-based research. Additionally, NIH applications for research grants must include (1) harm-benefit analyses for animal-based research proposals and (2) assurance that nonanimal methods for such research are not available.