We perform magnetohydrodynamic simulations in full general relativity (GRMHD) of quasi-circular, equal-mass, binary neutron stars that undergo merger. The initial stars are irrotational, n = 1 polytropes and are magnetized. We explore two types of magnetic-field geometries: one where each star is endowed with a dipole magnetic field extending from the interior into the exterior, as in a pulsar, and the other where the dipole field is initially confined to the interior. In both cases the adopted magnetic fields are initially dynamically unimportant. The merger outcome is a hypermassive neutron star that undergoes delayed collapse to a black hole (spin parameter a/MBH ~ 0.74) immersed in a magnetized accretion disk. About 4000M ~ 60(MNS/1.625M⊙) ms following merger, the region above the black hole poles becomes strongly magnetized, and a collimated, mildly relativistic outflow-an incipient jet-is launched. The lifetime of the accretion disk, which likely equals the lifetime of the jet, is Δ t ~ 0.1 (MNS/1.625M⊙) s. In contrast to black hole-neutron star mergers, we find that incipient jets are launched even when the initial magnetic field is confined to the interior of the stars.