LATAM airlines is launching a new direct route to Melbourne from Santiago, Chile later this year and kicking it off with some decent fares. Plenty of dates available (e.g. Oct 22 to November 11) from mid October. Plane is the 787 dreamliner.
Flights available through Expedia but I imagine you'd be able to score the same fares at other OTAs too.
Flights to other destinations in the region are also on sale. E.g. $1274 to Buenos Aries