A 1:1 adduct of chloranilic acid with 5,5'-dimethyl-2,2'-bipyridine, in which two kinds of molecules are connected by infinite hydrogen bond chains, exhibits a distinct dielectric phase transition when cooled. Below T(c)(=318 K) the hydrogen atoms participating in hydrogen bonding undergo long-range ordering and form an antiferroelectric-like state, taking a single minimum potential in the high-temperature phase (T>T(c)) due to the bifurcate hydrogen bond system. The proton-transfer phenomenon was clearly observed by electron density distribution analysis using a maximum entropy method of synchrotron x-ray diffraction data.