Pure rotational transitions of four isotopic species of the benzene-CO van der Waals complex have been observed in the microwave region between 8-18 GHz. Double resonance experiments on the parent species have been used to confirm the assignment of the spectrum resembling that of a symmetric top. The structure of the complex, with CO above the plane of benzene, has been determined from the measured moments of inertia for the isotopic species. Only an upper limit for the barrier to internal rotation of CO may be derived in the absence of transitions in excited internal rotation states.