Full geometric optimization of 3,4-benzobicyclo[3.2.1]-octadiene (BBOD) has been carried out by DFT/B3LYP method using the 6-311G(d), 6-311G(d,p) and 6-311+G(d,p) basis sets. The double bond is endo-pyramidalized and its two faces are not equivalent. The BBOD-Cl-2 system have been investigated by B3LYP /6-311+G(d,p) method and stable configurations determined. The stable Configurations of the BBOD center dot center dot center dot Cl-2 system correspond to BBOD center dot center dot center dot Cl-2(exo) and BBOD center dot center dot center dot Cl-2(endo) molecular complexes which are formed by the exo and endo orientation respectively of Cl-2 molecule to the double bond of BBOD in axial position. Exo-complex is relatively more stable than the endo-complex. Exo-chloronium cation was found to be more stable than endo-chloronium cation by the DFT method. Exo-facial selectivity is expected in the addition reaction to BBOD of chlorine. The non-classical delocalized chlorocarbonium cation(IV) is the most stable ion among the cationic intermediates, and the ionic addition reaction occurs via this cation. The mechanism of the addition reaction is also discussed.