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We investigate a generalization of the infinite time horizon linear quadratic regulator (LQR) for systems evolving on the special orthogonal group SO(3). Using Pontryagin's Maximum Principle, we derive the necessary conditions for optimality and the associated Hamiltonian equations. For a special class of weighting matrices, we show that the optimal feedback can be computed explicitly and we prove that the non differentiable value function is the viscosity solution of an appropriatedoi:10.3182/20100901-3-it-2016.00237 fatcat:t27xjzxuazf5tjpkudz733ro3m