Sometime during the 1870s to 1930s the USA had currency notes issued by banks chartered by the United States Government. The notes were backed by United States bonds the bank deposited with the United States Treasury.

National Bank of Honolulu, Hawaii (1929) 50 Dollar (front)

These notes were similar in overall appearance to most of the Federal Reserve Notes (the US Dollar notes we know today) with one important exception: the "title" (name) of the issuing "national bank", as well as the name of the town and state where the bank was located were printed on the notes. These notes also bore the signatures of that bank's president and cashier.

National Bank of Honolulu, Hawaii (1929) 50 Dollar (back)

National bank notes were retired as a currency type by the U.S. government in the 1930's during the great depression.

Sometimes these notes are called "hometown" notes, with their popularity deriving from the wide range of towns and cities that issued them. In the paper money hobby, especially in the U.S., these notes are avidly studied and collected. Some examples of rare banks, towns, states and combinations thereof are quite valuable.

Source: Wikipedia 'Natinal Bank Note'