We have made new observations of the bright (V = 14.7) infrared- selected QSO IRAS 13349 + 2438 (Beichman et al.), which provide important clues about the structure of the inner few parsecs of active galactic nuclei (AGNs). The principal observational facts are as follows: 1. There is high linear optical polarization, increasing with decreasing wavelength from 1.4% at 2.2 microns (K-band) to 8% at 0.36 microns (U-band). 2. The position angle of polarization is independent of wavelength in the optical region and is aligned with the direction of elongation of the r-band optical image, presumably the major axis of the host galaxy. This is probably true in the IR as well. 3. The position angle and degree of polarization of the broad Hα emission line is similar to that of the underlying continuum. 4. We find no variability of the polarization or flux density on time scales from days to months. 5. There is strong optical Fe II emission and the broad lines are relatively narrow (2100 km s^-1^). The emission from the narrow-line region is very weak. 6. The hydrogen broad-line ratios, Paα/Hα = 0.15 and Hα/Hβ = 5.9, are among the largest observed for a QSO (or even among Seyfert 1 galaxies.) If this indicates dust extinction, then comparison with these ratios in typical QSOs suggests E(B - V)~0.3. 7. The optical-UV continuum spectral energy distribution falls off very steeply toward the UV. The reddening required to match this continuum to those of typical luminous QSOs also corresponds to E(B-V) ~ 0.3. The high, time-independent polarization, its wavelength dependence, and its similarity in the continue- and broad Hα emission indicate that the polarization is caused by scattering in an anisotropic geometry. The polarized flux density spectrum looks like that of a normal high- luminosity QSO, with a strong UV excess; this is naturally explained if the scattered light has a degree of polarization independent of wavelength and has undergone little reddening The scatterers could be free electrons, or small dust grains with a range of scattering properties. The total observed spectrum is then the sum of this scattered, polarized spectrum and a reddened, transmitted spectrum. The decreased dilution of the scattered by the transmitted spectrum toward short wavelengths causes the rise in degree of polarization toward the UV. We derive a redening of E(B - V)~0.3 for the transmitted (direct) spectrum, depending on the intrinsic polarization of the scattered spectrum. We deduce a bipolar geometry for the inner regions of the QSO: a direct, but attenuated, AGN spectrum reaches the observer through an inclined, thick dusty disk that is parallel to the plane of the host galaxy, and probably between the broad- and narrow-line regions. Light escaping in polar directions is much less attenuated, with E(B - V)<0.05, and is scattered toward the observer and hence polarized parallel to the major axis of the host galaxy. IRAS 13349+2438 is the archetype of luminous highly polarized radio- quiet QSOs, and because of these properties is an important link in schemes that unify the apparently different kinds of AGNs by viewing angle, including the luminous "normal" QSOs, broad absorption line QSOs (BALQs), and (IRAS) ultraluminous AGNs. Specifically, we predict the spectroscopic and polarimetric properties of our model for IRAS 13349+2438 as it would appear at different inclinations and compare these predictions for unobscured luminous AGNs and AGNs suggested to contain "buried" QSO nuclei. A statistical comparison with samples of luminous AGNs chosen by orientation-independent infrared (eg., ~60 micron) flux density suggests that inclination is a key parameter in determining the appearance of these AGNs. Present optically selected samples of QSOs may be seriously incomplete, and investigation of more objects like IRAS 13349 + 2438 may tell us how incomplete they are.