In studying women's history, sometimes "famous firsts" are finely drawn - the honor gets at least a metaphorical asterisk explaining more details. Antoinette Brown Blackwell was the first woman ordained in America -- and the asterisk after that is that she was the first ordained by a congregation in a major or recognized Christian denomination. Olympia Brown (no relation) was long credited was being the first woman ordained with full denominational authority -- Antoinette Brown's ordination was by the congregation, which was the tradition in the Congregationalist denomination. Lydia Ann Moulton Jenkins's ordination with denominational authority (she, like Olympia Brown, was a Universalist) has been more recently found to be likely even earlier than Olympia Brown's. Antoinette Brown (later Blackwell) was ordained earlier than either.
Image from History of Woman Suffrage, Stanton et al. Modifications © 2003 Jone Johnson Lewis.