A portion of the CO dimer millimeter wave absorption spectrum has been studied by using our highly sensitive intracavity-jet OROTRON spectrometer in the frequency range from 131 to 174 GHz. By varying the CO concentration in the Ne/CO gas mixture feeding the supersonic jet expansion, the effective temperature of the beam could be changed, revealing a correlation between the observed line intensity and the relative energy of the respective lower state energy levels. Using this temperature dependence and the technique of combination differences together with the data from the infrared study of Brookes and McKellar [J. Chem. Phys. 111, 7321 (1999)], out of over 200 observed transitions, a total of 19 lines could be assigned. All assigned millimeter-wave transitions are tunneling transitions. They belong to four subbands, which connect seven lower energy levels with A(+) symmetry to ten previously unknown upper energy levels with A(-) symmetry. The A(+) and A(-) separation signifies the tunneling splitting of the CO stretching ground state v(CO) = 0 energy levels. The energies of all levels were determined to microwave accuracy. The discovered energy levels fall into two substates, corresponding to the projection K=0 and to K = 1 of the total angular momentum J onto the intermolecular axis. The effective intermolecular CO-CO separation for these new K = 0 and K = 1 states is 4.26 and 4.17 Angstrom, respectively.