In the favored progenitor scenario, Type Ia supernovae (SNe Ia) arise from a white dwarf accreting material from a non-degenerate companionstar. Soon after the white dwarf explodes, the ejected supernova material engulfs the companion star; two-dimensional hydrodynamicals imulations by Marietta et al. (2001) show that, in the interaction, the companion star carves out a conical hole of opening angle 30-40 degrees in the supernova ejecta. In this paper we use multi-dimensional Monte Carlo radiative transfer calculations to explore the observable consequences of an ejecta-hole asymmetry. We calculate the variation of the spectrum, luminosity, and polarization with viewing angle for the aspherical supernova near maximum light. We find that the supernova looks normal from almost all viewing angles except when one looks almost directly down the hole. In the latter case, one sees into the deeper, hotter layers of ejecta. The supernova is relatively brighter and has a peculiar spectrum characterized by more highly ionized species, weaker absorption features, and lower absorption velocities. The spectrum viewed down the hole is comparable to the class of SN 1991T-like supernovae. We consider how the ejecta-hole asymmetry may explain the current spectropolarimetric observations of SNe Ia, and suggest a few observational signatures of the geometry. Finally, we discuss the variety currently seen in observed SNe Ia and how an ejecta-hole asymmetry may fit in as one of several possible sources of diversity.