Australia set Sri Lanka an improbable 507 runs to win the second cricket Test early on the fourth day at Bellerive Oval here Monday.
Australian skipper Ricky Ponting, who remained unbeaten on 53 with Mike Hussey on 34, made the declaration 45 minutes before lunch giving his bowlers just over five sessions to bowl out the Sri Lankans.
The Sri Lankans, already one-down in the two-match series after a heavy innings and 40-run defeat in Brisbane, will have to create history to win the Hobart Test.
The world record fourth innings run chase for victory was 418 for seven by the West Indies against Australia in Antigua in May 2003.
The highest winning run chase at Bellerive was Australia's 369 for six against Pakistan in November 1999 -- which ranks as the fourth highest in Test history.
Opener Phil Jaques was the only wicket to fall on Monday caught on the point boundary by Michael Vandort off Lasith Malinga for 68.
Jaques was chasing his third consecutive century against Sri Lanka in the series.