We present optical spectropolarimetry obtained at the Keck-II 10-m telescope on 1998 March 7 UT along with total flux spectra spanning the first 494 days after discovery (1998 March 2 UT) of the peculiar type IIn supernova (SN) 1998S. The SN is found to exhibit a high degree of linear polarization, implying significant asphericity for its continuum-scattering environment. Prior to removal of the interstellar polarization, the polarization spectrum is characterized by a flat continuum (at p ≈ 2%) with distinct changes in polarization associated with both the broad (symmetric, half width near zero intensity 10, 000 km s −1 ) and narrow (unresolved, full width at half maximum < 300 km s −1 ) line emission seen in the total flux spectrum. When analyzed in terms of a polarized continuum with unpolarized broad-line recombination emission, an intrinsic continuum polarization of p ≈ 3% results, suggesting a global asphericity of 45% from the oblate, electron-scattering dominated models of Höflich (1991). The smooth, blue continuum evident at early times is shown to be inconsistent with a reddened, single-temperature blackbody, instead having a color temperature that increases with decreasing wavelength. Broad emission-line profiles with distinct blue and red peaks are seen in the total flux spectra at later times, suggesting a disk-like or ring-like morphology for the dense (n e ≈ 10 7 cm −3 ) circumstellar medium, generically similar to what is seen directly in SN 1987A, although much denser and closer to the progenitor in SN 1998S. Implications of the circumstellar scattering environment for the spectropolarimetry are discussed, as are the effects of uncertainty in the removal of interstellar polarization; the importance of obtaining multiple spectropolarimetric epochs to help constrain the interstellar polarization value is particularly stressed. Using information derived from the spectropolarimetry and the total flux spectra, an evolutionary scenario for SN 1998S and its progenitor are presented.