We report dielectric, thermodynamical, acoustic, and optical properties of a chiral molecular crystal, 1,1'-bi-2-naphthol 2-dimethylsulfoxide (BINOL•2DMSO). We find two successive phase transitions at T c1 = 190 K and T c2 = 125 K. The first transition at T c1 is characterized by an order-disorder transition of the guest molecules DMSO along with ferroelectricity.At the second transition of T c2 , the crystal structure deforms from tetragonal to monoclinic, leading to domain formation. Low-temperature x-ray diffraction suggests that the space group changes from P4 1 2 1 2 (P4 3 2 1 2) to P4 1 (P4 3 ) at T c1 , and down to P112 1 at T c2 .