The Cosmic Microwave Background (CMB) provides three strong but circumstantial pieces of evidence that the visible Universe was created by the superluminal inflation of a tiny volume of space: the near isotropy of the horizon, the flatness of space, and the phase-synchronicity of acoustic oscillations in the early universe. The goal of better understanding the origins of the Universe requires probing this epoch of Inflation directly. The most promising probe of Inflation is the unique signature that the GWB imprints on the polarization of the CMB. The amplitude of this signature depends on the energy-scale of Inflation. If the energy scale is typical of Grand Unification Theory (GUT) (10^15 > 3 x 10^16 GeV), the signature may be detectable. The signature of the GWB-induced polarization is expected to be less than an rms amplitude of ~300 nK of the CMB; more than two orders of magnitude below the amplitude of the temperature anisotropies that have only recently been resolved. Detection will require only modest angular resolution (~ 1 deg.), but will require long integration (~1 year) on a restricted (~3%) and contiguous patch of sky. The six-month night, the extremely dry and stable weather, and the precise rotation of the sky about the zenith make South Pole Station the ideal terrestrial site for this ambitious project. A CMB polarimeter (BICEP) uniquely capable of detecting the signature of the GWB is now under construction and will be available for deployment to the South Pole in 2003. The team that is building BICEP includes four senior experimentalists who have successfully fielded sophisticated bolometric instrumentation to the Antarctic. BICEP will operate simultaneously at 100 and 150 GHz in order to both minimize and recognize confusion from polarized astrophysical foregrounds. At these frequencies, a modest (and thus relatively easy to deploy and maintain) 20-cm primary aperture will provide a resolution of 1deg. at 100 GHz and 0.7 deg. at 150 GHz. By combining a new polarization-sensitive bolometric detector technology developed for Planck (2007 launch) with four independent levels of signal differencing and a carefully optimized observing strategy, BICEP will reach the current limit on CMB polarization in the first hour of integration, reach the sensitivity of Planck over 1% of the sky in the first week, and precisely measure CMB polarization on the critical angular scales of 1 deg. to 10 deg. BICEP will serve the broader community of cosmologists and astrophysicists by (i) pioneering an orders-of-magnitude improvement in this exciting new field, (ii) characterizing the diffuse astrophysical foregrounds that will ultimately limit measurements of this type (and which are of direct interest to Galactic astronomers), (iii) demonstrating new technologies and methodologies that promise to be of broad importance to millimeter-wave polarimetry, and (iv) providing excellent training for graduate students and postdoctoral fellows in labs which have a very strong track-record in this regard. Observational cosmology is currently enjoying a renaissance that has captured the public imagination, and serves as one of the most effective vehicles for stimulating interest in science in general. Detection of the signature of the GWB in the CMB would represent a triumph of fundamental physics and cosmology that would revolutionize our understanding of the origins of the Universe.