The third-order nonlinear optical susceptibility chi(3)(3omega) due to the intersubband transitions in the four-level AlInAs/GaInAs compositionally asymmetric coupled quantum well (CACQW) is investigated theoretically. The subband eigenenergy E(n) of the CACQW structure could be designed to form an equally spaced energy-level ladder. Since the eigenenergy spacing could be designed to resonate with the pumping source, the third-order nonlinear optical susceptibility could be greatly enhanced through the triple resonance. Based on the theoretical calculations, a magnitude of \chi(3)(3omega)\ as high as 2.2 X 10(5) (nm/V)2 can be achieved for the CACQW structure. This is a more than eight orders of magnitude enhancement as compared to that of the bulk value in GaAs. In addition to the design of CACQW structure, the triple resonance can also be achieved by biasing the CACQW under a proper electric field due to the large Stark effect of the CACQW structure.