Definition from Wiktionary, the free dictionary
Uncertain. Candidates are:
- A reference to William Buckley (1780-1856), a convict who escaped in Victoria in 1803 and lived among the Aborigines there for 30 years (survival in the bush was reckoned no chance). This is the most popular candidate, but earliest known usages date from the 1890s, some 30 years after his death. 
- From Buckley's and none (see that entry), presuming that expression derives from the Melbourne department store.
- A reference to Mr Buckley of the Bombala region of southern New South Wales, who sued the government over title to land, the action seeming to have little prospect of success.
- Again a reference to Mars Buckley, not in connection with Crumpton Nunn (as above, re Buckley's and none), but rather in relation to an 1893 run on banks, when Buckley ensured that the Bank of Australasia would have no chance of using his money to pay other depositors. The bank thus had “Buckley′s chance” of getting his money. This etymology is arguably the more likely since the phrase was first cited three years after this incident 
- (Australia, idiomatic, informal) A very small chance; no chance at all.
- Ozwords October 2000 at the Australian National University.
- ^ “Buckley′s Chance”, entry in 1970, Bill Wannan, Australian Folklore, Lansdowne Press, reprint 1979, ISBN 0-7018-1309-1, correspondence from a Mr F. Verdich of Rockdale, NSW.