An old bird is not to be caught with chaff. An experienced man, or one with his wits about him, is not to be deluded by humbug. The reference is to throwing chaff instead of bird-seed to allure birds. Hence—
“To chaff, ” meaning to banter, is a variant of chafe, to irritate.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894