WASHINGTON — The U.S. Supreme Court has agreed to hear an appeal from the nation’s television broadcasters and decide whether to shut down a new streaming service that sends shows to consumers via the Internet for a monthly fee.

Aereo, a Brooklyn-based startup distributor, uses small antennas to pick up over-the-air TV signals and allows a consumer to store them for later viewing. The company says its service is legal since it uses the signals that a homeowner with an old-fashioned antenna could pick up as well.

But broadcasters see a major threat to their industry because Aereo is re-transmitting their copyrighted programs and not paying for them. The biggest TV companies went to court in New York and sued Aereo for violating their copyrights.

But they lost last year when the 2nd Circuit Court of Appeals, in a 2-1 decision, said Aereo “transmits unique copies of broadcasts over the Internet” to individuals, so these are not “public” showings. Taking their appeal to the Supreme Court, the broadcasters said this decision, unless revised, would “profoundly affect, and potentially endanger, over-the-air broadcast television.”