A temperature dependence of H-1 NMR spin-lattice relaxation time in a zig-zag chain of chloride-bridged tetrakis(acetamidato)dirhodium was measured. The observed H-1 relaxation was well explained by the fluctuation of the magnetic dipolar interaction between proton and paramagnetic electron spins, where each unpaired spin is coupled by the one-dimensional antiferromagnetic interaction above 35 K. The slight change of the electronic state in the Rh dimer was observed below 35 K.