This paper proposes a comprehensive incremental program, Lunar Limb Observatory (LLO), for a return to the Moon, beginning with robotic missions and ending with a permanent lunar settlement. Several recent technological developments make such a program both affordable and scientifically valuable: robotic telescopes, the Internet, light-weight telescopes, shared- autonomy/predictive graphics telerobotic devices, and optical interferometry systems. Reasons for focussing new NASA programs on the Moon include public interest, Moon-based astronomy, renewed lunar exploration, lunar resources (especially helium-3), technological stimulus, accessibility of the Moon (compared to any planet), and dispersal of the human species to counter predictable natural catastrophes, asteroidal or cometary impacts in particular. The proposed Lunar Limb Observatory would be located in the crater Riccioli, with auxiliary robotic telescopes in M. Smythii and at the North and South Poles. The first phase of the program, after site certification, would be a series of 5 Delta-launched telerobotic missions to Riccioli (or Grimaldi if Riccioli proves unsuitable), emplacing robotic telescopes and carrying out surface exploration. The next phase would be 7 Delta-launched telerobotic missions to M. Smythii (2 missions), the South Pole (3 missions), and the North Pole (2 missions), emplacing robotic telescopes to provide continuous all-sky coverage. Lunar base establishment would begin with two unmanned Shuttle/Fitan-Centaur missions to Riccioli, for shelter emplacement, followed by the first manned return, also using the Shuttle/Fitan-Centaur mode. The main LLO at Riccioli would then be permanently or periodically inhabited, for surface exploration, telerobotic rover and telescope operation and maintenance, and support of Earth-based student projects. The LLO would evolve into a permanent human settlement, serving, among other functions, as a test area and staging base for the exploration, settlemen...