1953 in reference to experimental theater productions in New York City, from off (prep.) + Broadway. Even more experimental off-off-Broadway is attested by 1958.
off
offal
off-and-on
off-base
offbeat
off-Broadway
off-camera
off-chance
off-color
off-colour
off-duty
)window.location='https://www.paypal.com/cgi-bin/webscr?cmd=_donations&business=byronic106@yahoo.com&lc=US&item_name=Donation+to +Help+Keep+Etymonline+Free+and+Open&no_note=0&cn=&curency_code=USD&bn=PP-DonationsBF:btn_donateCC_LG.gif:NonHosted'){kind=link}