The Supreme Court agreed Monday to decide the constitutionality of a 2006 law making it a criminal offense to lie about being decorated for military service.

The Stolen Valor Act makes it unlawful to falsely represent, verbally or in writing, to have been “awarded any decoration or medal authorized by Congress for the Armed Forces of the United States, any of the service medals or badges awarded to the members of such forces, the ribbon, button, or rosette of any such badge, decoration, or medal, or any colorable imitation of such item.” The measure imposes penalties of up to a year in prison.

T...