The long lunar nights at the equatorial and mid-latitude regions of the Moon place severe limitations on the solar power and thermal management requirements of an unmanned lunar base. A solution to this problem is to locate sunlight-dependent facilities in polar regions where nights can be very short due to chance interactions of lunar topography and orbital mechanics. Based on analyses of Clementine and Earth-based radar imaging of the Moon, the authors conclude that the summit of Malapert Mountain near the South Pole has the best combination of factors for a sunlight-dependent lunar base. Using a commercial software product, they determined that the Mountain summit receives full or partial sunlight for 93% of the lunar year and always has the Earth in view for direct Earth-Moon communications. By exploiting these optimum conditions, a remotely operated base at the summit could coordinate the scientific exploration of the entire south polar region. The base could also expedite the development of a permanent utility infrastructure and facilities for human settlement. The authors conclude that the fortuitous and highly advantageous combination of physical factors of Malapert Mountain makes it the optimum site for beginning the human exploration and settlement of the Moon.