An effective Lagrangian for quark pairing in nonlinear chromodielectric models (CDM) is derived in the leading order. The effective pairing coupling depends explicitly on the confinement field, χ, of the CDM manifesting a confinement effect on color superconductivity. The self-consistent gap equations are constructed and solved for the color-flavor locked phase. The pairing coupling, for the quartic χ potential used in the calculations, is inversely proportional to the second power of the χ field and to the χ mass squared. In the chiral solution the quarks do not pair, but in the chiral breaking solution, where χ is small and the effective pairing interaction is stronger, it does show pairing. Our results indicate that the vector channel of the gap is weaker than the scalar one.