  We present Hubble WFC3/IR slitless grism spectra of a remarkably bright
$z\gtrsim10$ galaxy candidate, GN-z11, identified initially from
CANDELS/GOODS-N imaging data. A significant spectroscopic continuum break is
detected at $\lambda=1.47\pm0.01~\mu$m. 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 Ly$\alpha$
break redshifted to ${z_\mathrm{grism}=11.09^{+0.08}_{-0.12}}$, just $\sim$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
3x larger than L* measured at z~6-8. The Spitzer IRAC detections up to 4.5
$\mu$m of this galaxy are consistent with a stellar mass of
${\sim10^{9}~M_\odot}$. This spectroscopic redshift measurement suggests that
the 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.
