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We explore the origin of the Galactic high latitude black hole X-ray binaryXTE J1118+480, and in particular its birth location and the magnitude of thekick received by the black hole upon formation in the supernova explosion. Weconstrain the age of the companion to the black hole using stellar evolutioncalculations between 2 Gyr and 5 Gyr, making an origin in a globular clusterunlikely. We therefore argue that the system was born in the Galactic disk andthe supernova propelled it in its current high latitude orbit. Given thecurrent estimates on its distance, proper motion and radial velocity, weback-trace the orbit of XTE J1118+480 in the Galactic potential to infer thepeculiar velocity of the system at different disk crossings over the last 5Gyr. Taking into account the uncertainties on the velocity components, we inferan average peculiar velocity of 183 \pm 31 km/s. The maximum velocity which thebinary can acquire by symmetric supernova mass loss is about 100 km/s, which is2.7 sigma away from the mean of the peculiar velocity distribution. Wetherefore argue that an additional asymmetric kick velocity is required. Byconsidering the orientation of the system relative to the plane of the sky, wederive a 95% probability for a non null component of the kick perpendicular tothe orbital plane of the binary. The distribution of perpendicular velocitiesis skewed to lower velocities with an average of 93^{+55}_{-60} km/s.Comment: 6 pages, 6 figures, replaced with revised version, accepted for  publication in the Astrophysical Journa

Has the Black Hole in XTE J1118+480 Experienced an Asymmetric Natal Kick?