The NASA X-15 research airplane was one of the earliest aircraft to feature an adaptive control scheme, making its first flight in 1959. The program is largely considered a success, the one exception being the fatal accident that occurred on November 15, 1967. The circumstances which led to the anomalous behavior of the X-15 during that flight are reproduced using a fully nonlinear six-degree-of-freedom aircraft model and a detailed model of the original MH-96 adaptive controller. Using the lessons learned from the X-15 program as well as decades of work in the field of stable adaptive control, a provably correct (PC) adaptive controller is designed for the X-15. When subjected to the same conditions that caused the original MH-96 adaptive controller to fail, the PC adaptive controller is able to recover and complete the maneuver successfully.