We present Hubble WFC3/IR slitless grism spectra of a remarkably bright z gsim 10 galaxy candidate, GN-z11, identified initially from CANDELS/GOODS-N imaging data. A significant spectroscopic continuum break is detected at λ =1.47 ± 0.01 μm. The new grism data, combined with the photometric data, rule out all plausible lower redshift solutions for this source. The only viable solution is that this continuum break is the Lyα break redshifted to zgrism = 11.09⁺⁰.⁰⁸₋₀.₁₂ just ~400 Myr after the Big Bang. This observation extends the current spectroscopic frontier by 150 Myr to well before the Planck (instantaneous) cosmic reionization peak at z ~ 8.8, demonstrating that galaxy build-up was well underway early in the reionization epoch at z > 10. GN-z11 is remarkably, and unexpectedly, luminous for a galaxy at such an early time: its UV luminosity is 3× larger than L* measured at z ~ 6−8. The Spitzer IRAC detections up to 4.5 μm of this galaxy are consistent with a stellar mass of ~10⁹ M⊙. This spectroscopic redshift measurement suggests that James Webb Space Telescope (JWST) will be able to similarly and easily confirm such sources at z > 10 and characterize their physical properties through detailed spectroscopy. Furthermore, WFIRST, with its wide-field near-IR imaging, would find large numbers of similar galaxies and contribute greatly to JWST's spectroscopy, if it is launched early enough to overlap with JWST. ; 11 page(s)