United announced that they would be flying the Boeing 787 from Los Angeles to Melbourne six times per week starting October 26, 2014.
This new route for the 787 will be the longest route in which this aircraft will be flown at 7,927 miles.
Per this Forbes article, currently, the two longest 787 flights are operated by Ethiopian Airlines, but both stop in Rome on westbound routes from Addis Ababa to Washington and Toronto. Addis-Washington is 7,182 miles, while Addis-Toronto is 7,143 miles.
7,927 miles from Los Angeles to Melbourne is a long flight, so I would definitely want to be in one of the 36 Business First seats onboard this plane!