We report Nearby Supernova Factory observations of SN 2005g j, the second confirmed case of a ''hybrid'' Type Ia/IIn supernova, which we interpret as the explosion of a white dwarf interacting with a circumstellar medium. Our early-phase photometry of SN 2005gj shows that the interaction is much stronger than for the prototype, SN 2002ic. Our first spectrum shows a hot continuum with broad and narrow H emission. Later spectra, spanning over 4 months from outburst, show clear Type Ia features combined with broad and narrow H , H , H , and He i kk5876, 7065 in emission. At higher resolution, P Cygni profiles are apparent. Surprisingly, we also observe an inverted P Cygni profile for [O iii] k5007. We find that the light curve and measured velocity of the unshocked circumstellar material imply mass loss as recently as 8 years ago. The early light curve is well described by a flat radial density profile for the circumstellar material. However, our decomposition of the spectra into Type Ia and shock emission components allows for little obscuration of the supernova, suggesting an aspherical or clumpy distribution for the circumstellar material. We suggest that the emission-line velocity profiles arise from electron scattering rather than the kinematics of the shock. This is supported by the inferred high densities and the lack of evidence for evolution in the line widths. Ground-and spacebased photometry and Keck spectroscopy of the host galaxy are used to ascertain that the host galaxy has low metallicity (Z /Z < 0:3; 95% confidence) and that this galaxy is undergoing a significant star formation event that began roughly 200 AE 70 Myr ago. We discuss the implications of these observations for progenitor models and cosmology using Type Ia supernovae.