The total pi -electron energy of a conjugated molecule (within The framework of HMO approximation) can be calculated by its molecular graph. For the acyclic molecules, the extremal problem of some important types of conjugated molecules have been solved previously. This Letter for the first time deals with a type of cyclic conjugated molecule-benzenoid chains (hexagonal chains). We prove that in the set of all hexagonal chains with n hexagons, the linear polyacene has the minimal energy. Furthermore, a sharp lower bound of total pi -electron energies of the hexagonal chain is also obtained.