A steam monorail first appeared at the Centennial Exposition of 1876 in Philadelphia, Pennsylvania. It ran approximately 170 yards, and had a double-decker passenger configuration. Koerth-Baker points to a website with all the details, including cross-sections of how the train worked.
Ten years after the Centennial Exposition, another unique monorail appearing in Boston with a unique rounded shape and top speeds of 20 miles per hour.
Koerth-Baker links to other resources for early monorail information.