The U.S. Navy church pennant is flown aboard ships during church services aboard ship.  This pennant is authorized by Congress to be flown above the national ensign.  The pennant can also be used onshore, although not above the national ensign.  The use of such pennants dates back to at least 1827, when it was mentioned in a regulation, and some claims have usage going back to 1777.  For more information, see here, here, and Navy document NTP 13(B), section 1701.
Own work
Carl Lindberg