A federal appeals court threw out the FCC's rules on indecent speech Tuesday, in a big win for broadcasters that could lead to a new Supreme Court test of the government's power to control what is said on television and radio.

A three-judge panel of the Second U.S. Circuit Court of Appeals in New York said the Federal Communications Commission's indecency policies violate the First Amendment and are "unconstitutionally vague, creating a chilling effect that goes far beyond the fleeting expletives at issue here."

The...