H-1 nuclear magnetic resonance (NMR) measurements have been performed to study the proton dynamics associated with the antiferroelectric transition of a hydrogen-bonded single crystal of CsH3(SeO3)(2). Herein, H-1 NMR spectrum, shift, linewidth, and spin-lattice relaxation rate 1/T-1 are measured in the temperature range of 80-296 K with the c-axis parallel to a magnetic field of similar to 4.85 T. The spectrum exhibits a composite structure with two narrow peaks at 296 K; at a low temperature, this structure evolves into a single broad shape with three humps. This complex shape and evolution are deconvoluted into five or six components based on the number of inequivalent and disordered hydrogen sites. By estimating the chemical shift and linewidth for each proton site, we identify all peaks. The spin-lattice relaxation recovery exhibits a double-exponential behavior with two relaxation times, short T-1S and extremely large T-1L. Both T-1S and T-1L follow Arrhenius behavior. From the respective 1/T-1(T), the activation energies for proton motion are measured to be small: 1.16 +/- 0.1 and 0.83 +/- 0.06 kJ/mol for T-1S and T-1L, respectively. While the static NMR data, chemical shift and linewidth, show no evidence for the transition, the dynamic data 1/T-1L, highlights a clear increase across T-N = 145 K, which is possibly a signature of the transition.