Novel feature of guided modes in the chiral nihility (the permittivity and permeability are simultaneously zero) cladding fiber were investigated theoretically. The electromagnetic fields in the chiral nihility cladding fiber were presented. Dispersion equations and power of guided modes were derived. Dispersion curves of guided modes were plotted for different chirality parameters. The effect of chirality parameter on power was discussed. Some novel feature are found: surface wave mode and single-mode operation region, double propagation constant, mode intersection and energy store, especially, exotic backward wave mode of which the power is negative both in the core and cladding.