We present a fully relativistic theoretical treatment of the process of dielectronic recombination (DR) with emission of two photons. In the case of KLL DR into hydrogen-like ions, the system is not stable until both electrons are de-excited with the emission of two photons. On the basis of a projection operator formalism, perturbative expressions for the cross sections are derived. The results for the total cross section for hydrogen-like uranium are presented and compared to those which have been obtained in a theory considering only one photon transition. In addition, the angular distribution of the two photons and their correlation are examined.