Wind turbines operate in highly turbulent environments resulting in aerodynamic loads that can easily excite turbine structural modes, potentially causing component fatigue and failure. Two key technology drivers for turbine manufacturers are increasing turbine up time and reducing maintenance costs. Since the trend in wind turbine design is towards larger, more flexible turbines with lower frequency structural modes, manufacturers will want to develop methods to operate in the presence of these modes. Accurate models of the dynamic characteristics of new wind turbines are often not available due to the complexity and expense of the modeling task, making wind turbines ideally suited to adaptive control. In this paper, we develop theory for adaptive control with rejection of disturbances in the presence of modes that inhibit the controller. We use this method to design an adaptive collective pitch controller for a high-fidelity simulation of a utility-scale, variable-speed wind turbine operating in Region 3. The objective of the adaptive pitch controller is to regulate generator speed, accommodate wind gusts, and reduce the interference of certain structural modes in feedback. The control objective is accomplished by collectively pitching the turbine blades. The adaptive pitch controller for Region 3 is compared in simulations with a baseline classical Proportional Integrator (PI) collective pitch controller