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.