1. Statement I: Benzene undergoes electrophilic aromatic substitution with Cl$_2$/AlCl$_3$, forming chlorobenzene (C$_6$H$_5$Cl), as AlCl$_3$ generates Cl$^+$ electrophile, correct.
2. Statement II: With Cl$_2$ under UV light, benzene undergoes free radical addition, forming hexachlorocyclohexane (C$_6$H$_6$Cl$_6$), not electrophilic substitution, incorrect.
3. Electrophilic substitution requires electrophile attack on aromatic ring, maintaining aromaticity, unlike radical addition.
4. Thus, the answer is (3) Statement I is correct, but statement II is not correct.