We've had several posts over the years about Allen and chanting, and most famously (most infamously?) his chanting of the Hare Krishna chant - "Hare Krishna, Hare Krishna, Krishna Krishna, Hare Hare, Hare Rama, Hare Rama, Rama Rama, Hare Hare". For a fuller, and more detailed, account of his involvement with this mantra (and indeed his involvement, during the 'Sixties, with Swami Srila Prabhupada and with the whole ISKCON movement), see here.
Jonas Mekas' 4-minute film from 1966 is one illustration - here's another one - an hommage,
straight up on You Tube, by "rose7art" (sic) - reductive, but curiously effective in its simplicity - And who can forget Allen in 1968 on the William Buckley show? - see here.