An explicit combinatorial expression is obtained for the Zhang-Zhang polynomial (also known as “Clar cover polynomial”) of a large class of pericondensed benzenoid systems, the multiple linear hexagonal chains M_n,m. By means of this result, various problems encountered in the Clar theory of M_n,m are also resolved: counting of Clar and Kekulé structures, determining the Clar number, and calculating the sextet polynomial.