Proton transfer in a hydrated crystal of a squaric acid derivative, p-phenylenebis(squaric acid) (PBSQ), was investigated by means of ac dielectric measurements. The crystal consisted of PBSQ monoanions and protonated water dimer (H5O2+) counter cations, and a highly symmetric, one-dimensional hydrogen-bonded chain was formed through strong (OHO-)-O-... ionic hydrogen bonding between deprotonated PBSQ moieties. The permittivity of the hydrated crystal was nearly temperature independent (epsilon' similar to 9), but the deuterated crystal exhibited a Curie-Weiss type temperature dependence and underwent depression of the permittivity at 28 K, which is the characteristic of an (anti)ferroelectric phase transition. Thus, we conclude that the dielectric response of the hydrated PBSQ crystal originates from proton transfer along the intermolecular hydrogen bond and that the temperature-independent dielectric behavior can be interpreted in terms of quantum paraelectricity.