A molecule has a center of symmetry when, for any atom in the molecule, an identical atom exists diametrically opposite this center an equal distance from it(Wikipedia).
A center of symmetry is said to exist in a molecule when reflection of all parts of the molecule through the center of symmetry produces an indistinguishable configuration(Housecroeft and Sharpe,2012)
Obviously, the Cl2 molecule has a center of symmetry, hence it is symmetrical. Reflection of the molecules through its center of symmetry produces an indistinguishable configuration.
