We extend to the context of (closed, orientable, locally orientable) 3-orbifolds the famous Haken-Kneser-Milnor theorem, according to which every 3-manifold splits as a connected sum of prime ones, and the summands are unique. We show that the statement itself of the generalized theorem must be given with a little care, and we explain why the direct analogue of the argument proving the theorem in the manifold case, based on the notion of maximal essential system of spheres, cannot give the desired conclusion for orbifolds. We then outline the approach through which we have proved existence and uniqueness of the splitting.