We present a spectroscopic redshift measurement of a very bright Lyman break galaxy at z=7.7302+-0.0006 using Keck/MOSFIRE. The source was pre-selected photometrically in the EGS field as a robust z~8 candidate with H=25.0 mag based on optical non-detections and a very red Spitzer/IRAC [3.6]-[4.5] broad-band color driven by high equivalent width [OIII]+Hbeta line emission. The Lyalpha line is reliably detected at 6.1 sigma and shows an asymmetric profile as expected for a galaxy embedded in a relatively neutral inter-galactic medium near the Planck peak of cosmic reionization. The line has a rest-frame equivalent width of EW0=21+-4 A and is extended with V_FWHM=360+90-70 km/s. The source is perhaps the brightest and most massive z~8 Lyman break galaxy in the full CANDELS and BoRG/HIPPIES surveys, having assembled already 10^(9.9+-0.2) M_sol of stars at only 650 Myr after the Big Bang. The spectroscopic redshift measurement sets a new redshift record for galaxies. This enables reliable constraints on the stellar mass, star-formation rate, formation epoch, as well as combined [OIII]+Hbeta line equivalent widths. The redshift confirms that the IRAC [4.5] photometry is very likely dominated by line emission with EW0(OIII+Hbeta)= 720-150+180 A. This detection thus adds to the evidence that extreme rest-frame optical emission lines are a ubiquitous feature of early galaxies promising very efficient spectroscopic follow-up in the future with infrared spectroscopy using JWST and, later, ELTs. ; Comment: 6 pages, 4 figures, small updates to match ApJL accepted version