A double-resonance experiment of Cs-133 NMR was performed in the three-dimensionally ordered phase of a triangular-lattice Ising-like antiferromagnet CsCoCl3. The spin inversion in the Co2+ chain was detected by observing the change of the internal magnetic field at the Cs site. The inversion times, which are of the order of 10(2) s at liquid helium temperatures, were obtained from an analysis by the rate equations. This spin inversion is a slow dynamics and is interpreted as a result of the sublattice switching arisen from the movement of the ferrimagnetic domain wall in the c plane.