A precise value for cosmic background radiation (CBR) temperature at 2.64 mm is reported using interstellar CN molecules in absorption in the direction of Zeta Oph. A search for CN emission at 2.64 mm makes it possible to set a strong limit on local excitation sources that could elevate the population of the 2.64 mm rotational states above that expected from the cosmic background radiation. To one standard deviation, observations show that T(loc) is not above 31 mK. A reanalysis of data previously reported has improved the precision of the optical equivalent widths so that this source of uncertainty is now 13.3 mK. Uncertainties in the saturation correction model add to the error budget. The final value for T(CBR) = 2.796(+0.014, -0.039) K. 27 refs.