In this paper, the aeroelastic stability of a hingeless rotor blade in hover is investigated. The blade is modeled using the geometrically exact, fully intrinsic beam equations, whereas the aerodynamic loads applied on the blade are simulated based on the quasi-steady Greenberg aerodynamic theory. Using the generalized differential quadrature method, the resultant coupled aeroelastic equations are discretized and solved, and the eigenvalues of the linearized system are determined. By inspecting the eigenvalues, the stability of the system is examined for variations in different parameters. The obtained results are validated through comparison against those reported in the literature. Furthermore, the effects of offset of the aerodynamic center from the reference axis, the precone angle, the lead-lag frequency, static stall, and the drag coefficient on the stability boundaries of the system are evaluated. It is found that, by using the geometrically exact, fully intrinsic beam equations along with the generalized differential quadrature method, the aeroelastic instabilities of the hingeless rotor blades in hover can be determined accurately.