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 $a/m=0.75$ (m is the black hole Christodoulou mass) aligned with the orbital angular momentum, and the neutron star is an irrotational ${\Gamma }=2$ polytrope. About two orbits prior to merger (at time $t={{t}_{B}}$), we seed the neutron star with a dynamically weak interior dipole magnetic field that extends into the stellar exterior. At $t={{t}_{B}}$, the exterior has a low-density atmosphere with a constant plasma parameter $\beta \equiv {{P}_{{\rm gas}}}/{{P}_{{\rm mag}}}$. Varying β at tB in the exterior from 0.1 to 0.01, we find that at a time $\sim 4000M\sim 100({{M}_{{\rm NS}}}/1.4{{M}_{\odot }})\;{\rm ms}$ (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 ${\Delta }t\sim 0.5({{M}_{{\rm NS}}}/1.4{{M}_{\odot }})$ s. Our simulations furnish the first explicit examples in GRMHD that show that a jet can emerge following a BHNS merger.