Analytical solutions of a double cladding (W type) chiral optical fiber which both core and claddings are chiral media have been presented. The solutions of guided modes and modal characteristic equation are derived. The effects of chirality on dispersion curves and cut off freqencies of guided modes are studied by numerical method.The single mode operation can be supported by using chiral core material in the double cladding optical fiber or using chiral cladding material in the single cladding optical fiber.