Following recent abundance measurements of Mg, Al, Ca, Fe, and Ni in the black hole X-ray binary XTE J1118+480 using medium-resolution Keck II ESI spectra of the secondary star, we perform a detailed abundance analysis including the abundances of Si and Ti. These element abundances, which are higher than solar, indicate that the black hole in this system formed in a supernova event, whose nucleosynthetic products could pollute the atmosphere of the secondary star, providing clues to the possible formation region of the system, either Galactic halo, thick disk, or thin disk. We explore a grid of explosion models with different He core masses, metallicities, and geometries. Metal-poor models associated with a formation scenario in the Galactic halo provide unacceptable fits to the observed abundances, allowing us to reject a halo origin for this X-ray binary. The thick-disk scenario produces better fits, although they require substantial fallback and very efficient mixing processes between the inner layers of the explosion and the ejecta, making an origin in the thick disk quite unlikely. The best agreement between model predictions and the observed abundances is obtained for metal-rich progenitor models. In particular, non-spherically symmetric models are able to explain, without strong assumptions of extensive fallback and mixing, the observed abundances. Moreover, asymmetric mass ejection in a supernova explosion could account for the required impulse necessary to launch the system from its formation region in the Galactic thin disk to its current halo orbit.