Has the black hole in XTE J1118+480 experienced an asymmetric natal kick?

We explore the origin of the high Galactic latitude black hole X-ray binary XTE J1118+480 and in particular its birth location and the magnitude of the kick received by the black hole upon formation in the supernova explosion. Our analysis is constrained by the evolutionary state of the companion star, the observed limits on the orbital inclination, the Galactic position, and the peculiar velocity of the binary system. We constrain the age of the companion to the black hole using stellar evolution calculations between 2 and 5 Gyr, making an origin in a globular cluster unlikely. We therefore argue that the system was born in the Galactic disk, in which case the supernova must have propelled it in its current high-latitude orbit. Given the current estimates on its position in the sky, proper motion, and radial velocity, we back-trace the orbit of XTE J1118+480 in the Galactic potential to infer the peculiar velocity of the system at different disk crossings over the last 5 Gyr. Taking into account the uncertainties on the velocity components, we infer that the peculiar velocity required to change from a Galactic disk orbit to the currently observed orbit is 183 +/- 31 km s(-1). The maximum velocity that the binary can acquire by symmetric supernova mass loss is about 100 km s(-1), which is 2.7 sigma away from the mean of the peculiar velocity distribution. We therefore argue that an additional asymmetric kick velocity is required. By considering the orientation of the system relative to the plane of the sky, we derive a 95% probability for a nonnull component of the kick perpendicular to the orbital plane of the binary. The distribution of perpendicular velocities is skewed to lower velocities with an average of 93(-60)(+55) km s(-1). These estimates are independent of the age of the system but depend quite sensitively on the kinematic parameters of the system. A better constraint on the asymmetric kick velocity requires an order-of-magnitude improvement in the measurement of the current space velocity of the system.