The Advanced Technology Large Aperture Space Telescope (ATLAST) team identified five key technology areas to enable candidate architectures for a future large-aperture ultraviolet/optical/ infrared (LUVOIR) space observatory envisioned by the NASA Astrophysics 30-year roadmap, "Enduring Quests, Daring Visions." The science goals of ATLAST address a broad range of astrophysical questions from early galaxy and star formation to the processes that contributed to the formation of life on Earth, combining general astrophysics with direct-imaging and spectroscopy of habitable exoplanets. The key technology areas are internal coronagraphs, starshades (or external occulters), ultra-stable large-aperture telescope systems, detectors, and mirror coatings. For each technology area, we define best estimates of required capabilities, current state-of-the-art performance, and current technology readiness level (TRL), thus identifying the current technology gap. We also report on current, planned, or recommended efforts to develop each technology to TRL 5.