We report on optical spectroscopic observations of the X-ray Transient XTE J1118+480 covering the period from April 7 , 2000 to July 4 , 2000 . The spectrum is characterized by weak , broad , double-peaked Balmer and He lines on top of a blue continuum of slope p \approx 1 / 3 , as expected for an optically-thick accretion disk . The weak Bowen blend seen in our spectra may indicate a low metallicity for the source . The presence of a partial S-wave pattern in the He ii \lambda 4686 line appears consistent with the reported photometric period P _ { orb } = 4.1 hr for XTE J1118+480 . By using a combination of Doppler mapping and various theoretical arguments , we constrain plausible orbital parameters for the system : a mass ratio 0.02 \hbox to 0.0 pt { \lower 2.5 pt \hbox { $ \sim$ } } \raise 1.5 pt \hbox { $ < $ } q % \hbox to 0.0 pt { \lower 2.5 pt \hbox { $ \sim$ } } \raise 1.5 pt \hbox { $ < $ } 0.1 , an inclination i \hbox to 0.0 pt { \lower 2.5 pt \hbox { $ \sim$ } } \raise 1.5 pt \hbox { $ > $ } 70 ^ { o } for a neutron star primary , or 30 ^ { o } \hbox to 0.0 pt { \lower 2.5 pt \hbox { $ \sim$ } } \raise 1.5 pt \hbox { $ < $ } i % \hbox to 0.0 pt { \lower 2.5 pt \hbox { $ \sim$ } } \raise 1.5 pt \hbox { $ < $ } 50 ^ { o } for a black hole primary with a mass between 4 and 10 ~ { } M _ { \odot } . Ca ii absorption features observed at very high resolution constrain the interstellar hydrogen absorption column \log [ N _ { H { \sc i } } ~ { } ( { ~ { } cm ^ { -2 } } ) ] \approx 20.45 \pm 0.2 and the identification of three absorbing clouds indicate a distance to the source \hbox to 0.0 pt { \lower 2.5 pt \hbox { $ \sim$ } } \raise 1.5 pt \hbox { $ < $ } 1 kpc , assuming the line-of-sight to XTE J1118+480 has average high-latitude properties . These results are discussed in the context of previous multiwavelength observations of this unusual system .