An aerodynamic shape optimization technique has been developed for helicopter rotor blades in hover based on a continuous adjoint method on unstructured meshes. For this purpose, the Euler flow solver and the adjoint sensitivity analysis were formulated on the rotating frame of reference. To handle the repeated evaluation of the flow solution and the sensitivity analysis efficiently, the flow and adjoint solvers were parallelized using a domain decomposition strategy. A solution-adaptive mesh refinement technique was adopted to better resolve the tip vortex. Applications were made to the aerodynamic shape optimization of the Caradonna-Tung rotor blade and the UH-60 rotor blade. The results showed that the present method is effective in determining optimum aerodynamic configurations of rotor blades in hover, which require minimum inviscid torque while maintaining the desired thrust level at transonic flight conditions.