Green’s Dictionary of Slang

a general term of dismissal or negation, no hope or possibility whatsoever.

1908		B. Fisher A. Mutt in Blackbeard Compilation (1977) 107: Just think of a two ton Paderewski trying to reach the keyboard with his fingers. No chance.
1912		Sport (Adelaide) 31 Aug. 14/2: They Say [...] That Wonga thinks that when he secures that medal he will be admitted to the Saturday night hoppers. No chance, Wonga.
1915		Van Loan ‘On Account of a Lady’ in Taking the Count 137: ‘Some fight tomorrow night,’ said Split-tooth tentatively. ‘Those big hams [...] No chance – I could lick ’em myself.’.
1937		J. Curtis There Ain’t No Justice 17: ‘How’s chances for a fag?’ ‘No chance.’.
1971		E.E. Landy Underground Dict. (1972).
1989		Beano Special No. 13 n.p.: Spain? Ho-ho! No chance!
1999		K. Sampson Powder 156: Ha! No chance!