We have used the rocket-borne Wide-Field Imaging Survey Polarimeter (WISP) to image a 1.5 deg. by 4.8 deg. area of the western side of the LMC at a wavelength of 215 nm and a resolution of 1' x 1.5'. These are the first wide-field ultraviolet polarimetric images in astronomy. We find the UV background light of the LMC to be linearly polarized at levels ranging from 0.04 to ~0.4. In general, the polarization in a pixel increases as the flux decreases; the weighted mean value of polarization across the WISP field is 0.126 +/- 0.023. The LMC's diffuse UV background, in uncrowded areas, rises from a minimum of 23.6 +/- 0.5 mag/arcsec**2 to 23.1 +/- 0.2 in regions near the bright OB associations. We use our polarization maps to investigate the geometry of the interstellar medium in the LMC, and to search for evidence of a significant contribution of scattered light from OB associations to the diffuse galactic light of the LMC. Through a statistical analysis of our polarization map, we identify 9 regions of intense UV emission which may be giving rise to scattering halos in our image. We find that starlight from the N11 complex and the LH 15 association are the strongest contributors to the scattered light component of the LMC's diffuse galactic light. This region of the northwestern LMC can be thought of as a kiloparsec-scale reflection nebula, in which OB stars illuminate distant dust grains, which scatter the light into our sightline. In contrast, the polarization map does not support the scattering of light from the large B2 complex in the southern WISP field; this effect may be astrophysical, or it may be the result of bias in our analysis. Comment: Accepted to AJ. 14 pages, 5 figures