The optical properties of the ice at the geographical South Pole have been investigated at depths between 0.8 and 1 kilometer. The absorption and scattering lengths of visible light ( approximately 515 nanometers) have been measured in situ with the use of the laser calibration setup of the Antarctic Muon and Neutrino Detector Array (AMANDA) neutrino detector. The ice is intrinsically extremely transparent. The measured absorption length is 59 +/- 3 meters, comparable with the quality of the ultrapure water used in the Irvine-Michigan-Brookhaven and Kamiokande proton-decay and neutrino experiments and more than twice as long as the best value reported for laboratory ice. Because of a residual density of air bubbles at these depths, the trajectories of photons in the medium are randomized. If the bubbles are assumed to be smooth and spherical, the average distance between collisions at a depth of 1 kilometer is about 25 centimeters. The measured inverse scattering length on bubbles decreases linearly with increasing depth in the volume of ice investigated.