  We report the detection of pulsed gamma-rays from the young, spin-powered
radio pulsar PSR J2021+3651 using data acquired with the Large Area Telescope
(LAT) on the Fermi Gamma-ray Space Telescope (formerly GLAST). The light curve
consists of two narrow peaks of similar amplitude separated by 0.468 +/- 0.002
in phase. The first peak lags the maximum of the 2 GHz radio pulse by 0.162 +/-
0.004 +/- 0.01 in phase. The integral gamma-ray photon flux above 100 MeV is
(56 +/- 3 +/- 11) x 10^{-8} /cm2/s. The photon spectrum is well-described by an
exponentially cut-off power law of the form dF/dE = kE^{-\Gamma} e^(-E/E_c)
where the energy E is expressed in GeV. The photon index is \Gamma = 1.5 +/-
0.1 +/- 0.1 and the exponential cut-off is E_c = 2.4 +/- 0.3 +/- 0.5 GeV. The
first uncertainty is statistical and the second is systematic. The integral
photon flux of the bridge is approximately 10% of the pulsed emission, and the
upper limit on off-pulse gamma-ray emission from a putative pulsar wind nebula
is <10% of the pulsed emission at the 95% confidence level. Radio polarization
measurements yield a rotation measure of RM = 524 +/- 4 rad/m^2 but a poorly
constrained magnetic geometry. Re-analysis of Chandra data enhanced the
significance of the weak X-ray pulsations, and the first peak is roughly
phase-aligned with the first gamma-ray peak. We discuss the emission region and
beaming geometry based on the shape and spectrum of the gamma-ray light curve
combined with radio and X-ray measurements, and the implications for the pulsar
distance. Gamma-ray emission from the polar cap region seems unlikely for this
pulsar.
