The authors describe the design of a new polarization sensitive receiver, spt-3g, for the 10-meter South Pole Telescope (spt). The spt-3g receiver will deliver a factor of approximately 20 improvement in mapping speed over the current receiver, spt-pol. The sensitivity of the spt-3g receiver will enable the advance from statistical detection of B-mode polarization anisotropy power to high signal-to-noise measurements of the individual modes, i.e., maps. This will lead to precise (approximately 0.06 eV) constraints on the sum of neutrino masses with the potential to directly address the neutrino mass hierarchy. It will allow a separation of the lensing and in ationary B-mode power spectra, improving constraints on the amplitude and shape of the primordial signal, either through spt-3g data alone or in combination with bicep2/keck, which is observing the same area of sky. The measurement of small-scale temperature anisotropy will provide new constraints on the epoch of reionization. Additional science from the spt-3g survey will be signicantly enhanced by the synergy with the ongoing optical Dark Energy Survey (des), including: a 1% constraint on the erentialbias Doppler signal from pairs of galaxy clusters that will test General Relativity on approximately 200Mpc scales, and improved of cosmological constraints from the abundance of clusters of galaxies.