We present the first detection of carbon monoxide (CO) in a damped Lyman-α system (DLA) at z abs = 2.41837 toward SDSS J143912.04+111740.5. We also detected H 2 and HD molecules. The measured total column densities (in log units) of H i, H 2 , and CO are 20.10± 0.10, 19.38± 0.10, and 13.89± 0.02, respectively. The molecular fraction, f = 2N(H 2 )/(N(H i)+2N(H 2 )) = 0.27−0.08 , is the highest among all known DLAs. The abundances relative to solar of S, Zn, Si, and Fe are −0.03 ± 0.12, +0.16 ± 0.11, −0.86 ± 0.11, and −1.32 ± 0.11, respectively, indicating a high metal enrichment and a depletion pattern onto dust-grains similar to the cold ISM of our Galaxy. The measured N(CO)/N(H 2 ) = 3 × 10 −6 is much less than the conventional CO/H 2 ratio used to convert the CO emission into gaseous mass but is consistent with what is measured along translucent sightlines in the Galaxy. The CO rotational excitation temperatures are higher than those measured in our Galactic ISM for similar kinetic temperature and density. Using the C i fine structure absorption lines, we show that this is a consequence of the excitation being dominated by radiative pumping by the cosmic microwave background radiation (CMBR). From the CO excitation temperatures, we derive T CMBR = 9.15 ± 0.72 K, while 9.315 ± 0.007 K is expected from the hot big-bang theory. This is the most precise high-redshift measurement of T CMBR and the first confirmation of the theory using molecular transitions at high redshift.