Catalysis of the reaction: 1-chloro-2,2-bis(4-chlorophenyl)ethane = HCl + unsym-bis(4-chlorophenyl)ethene. 1-chloro-2,2-bis(4-chlorophenyl)ethane is also known as DDMS; unsym-bis(4-chlorophenyl)ethene is also known as DDNU.