The Stratospheric Observatory for Infrared Astronomy (SOFIA) will be a 2.5-m clear-aperture telescope mounted in an open cavity in a modified Boeing 747 SP aircraft. SOFIA represents the next generation of the NASA Ames Research Center's infrared astronomy program. The existing airborne infrared telescope, the Kuiper Airborne Observatory (KAO), is a 0.91-m-aperture telescope flown on a Lockheed C-141 aircraft. The SOFIA telescope will have approximately eight times the sensitivity and three times the resolution of the KAO, and will be able to detect all of the far-infrared point sources detected by the Infrared Astronomical Satellite in 1983. A number of studies have been performed on the design of a large-aperture telescope capable of operating in the environment of an aircraft flying at 41,000 ft at Mach 0.85 while looking at astronomical sources through an open port. SOFIA poses a number of serious technical challenges for both the telescope designer and the system designer. This paper addresses one of these challenges, namely, the design of the telescope's primary mirror. Using new Russian technology will permit the fabrication of a lightweight, 2.7-m-diameter, f/1.3, primary mirror made of silicon carbide. The mirror and its graphite-aluminum mount will weight 650 kg, will not require any kind of active figure control or gravity sag compensation, will have a thermal time constant less than any other material, and will meet or exceed all of the requirements for the SOFIA mission.