The phrase "chanting man" occurs in the United Service Journal for August 1837.

The piece is "Saturday Night at Sea, in 1837." The men are entertaining each other with yarns and songs. The narrator calls upon someone to sing....

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...John Tendersides, who was the only man on the forecastle who looked like a seaman... his hair was bushy and thick, and he was a fine broad-shouldered fellow, big enough and ugly enough to have fought a Spanish bull, or turned a tiger inside out. 'Now,' said I to myself, 'I shall get a stave such as I used to hear,' for his voice was as gruff as a coal-heaver's after he has cleared a collier and been the chanting man of the crew.
// (pp. 481-2)