The airline has six of the fuel-efficient jets, which were grounded in mid-January in response to two fires in the lithium-ion battery compartments.
Four of airline's six 787 jets have been outfitted with graded battery systems and are ready to fly, WMAQ-TV, Chicago, reported.
The first route for the 787 was a morning flight from Houston to Chicago. The airline said it would proceed cautiously, using the jet, initially, for domestic flights over land.
That will change June 10, when the carrier will use the jet for an international fight -- a flight from Denver to Tokyo.
Airlines can best take advantage of the 787's fuel efficiency on longer flights.
Boeing says the 787 Dreamliner is 20 percent more fuel efficient than similarly sized jets.
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