General relativistic orbital decay in a seven-minute-orbital-period eclipsing binary system

General relativity predicts that short orbital period binaries emit significant gravitational radiation, and the upcoming Laser Interferometer Space Antenna (LISA) is expected to detect tens of thousands of such systems; however, few have been identified, and only one is eclipsing--the double white dwarf binary SDSS J065133.338+284423.37, which has an orbital period of 12.75 minutes. Here, we report the discovery of an eclipsing double white dwarf binary system with an orbital period of only 6.91 minutes, ZTF J153932.16+502738.8. This system has an orbital period close to half that of SDSS J065133.338+284423.37 and an orbit so compact that the entire binary could fit within the diameter of the planet Saturn. The system exhibits a deep eclipse, and a double-lined spectroscopic nature. We observe rapid orbital decay, consistent with that expected from general relativity. ZTF J153932.16+502738.8 is a significant source of gravitational radiation close to the peak of LISA's sensitivity, and should be detected within the first week of LISA observations.