The Bureau of Engraving and Printing has never been
authorized to print a $3 note. However, during the early 1800's, banks operating under Federal or State charters issued notes of that denomination. These notes were printed by private contractors and were not obligations of the federal government. There is a permanent exhibit about the $3 bill on display in "Philadelphia's Independence Hall."
source: U.S. Bureau of Engraving and Printing