We perform magnetohydrodynamic simulations in full general relativity (GRMHD) of a binary black hole–neutron star (BHNS) on a quasicircular orbit that undergoes merger. The binary mass ratio is 3:1, the black hole initial spin parameter (m is the black hole Christodoulou mass) aligned with the orbital angular momentum, and the neutron star is an irrotational polytrope. About two orbits prior to merger (at time ), we seed the neutron star with a dynamically weak interior dipole magnetic field that extends into the stellar exterior. At , the exterior has a low-density atmosphere with a constant plasma parameter . Varying β at tB in the exterior from 0.1 to 0.01, we find that at a time (M is the total (ADM) mass) following the onset of accretion of tidally disrupted debris, magnetic winding above the remnant black hole poles builds up the magnetic field sufficiently to launch a mildly relativistic, collimated outflow—an incipient jet. The duration of the accretion and the lifetime of the jet is s. Our simulations furnish the first explicit examples in GRMHD that show that a jet can emerge following a BHNS merger.