Pristine graphene possesses high electrical mobility, but its low charge carrier density severely limits its technological significance. Past efforts to increase graphenes carrier density via chemical doping have shown limited successes, accompanied by substantial reductions in the mobility caused by disordered dopants. Here, based on first-principles calculations, we propose to grow graphene on Cu(111) via self-assembly of C5NCl5 molecular precursors to achieve high-density (1/6) and highly ordered nitrogen doping. Such a process relies on the elegant concerted roles played by the London dispersion, chemical, and screened Coulomb repulsive forces in enhancing molecular adsorption, facilitating easy dechlorination, and dictating the overall orientation of the C5N radicals, respectively. Further growth from the orientationally correlated graphene islands is accompanied by significantly minimized density of grain boundaries as the grains coalesce to form larger N-doped graphene sheets, which are further shown to possess superb electronic properties for future device applications. Initial kinetic processes involved in N-doped graphene growth using C5NH5 precursors are also investigated and contrasted with that of C5NCl5.