We have used absorption of orthoformaldehyde (H2CO) toward the giant H II region W51A (G49.5-0.4) as a remote probe of the cosmic microwave background (CMB) at a distance of 7.5 kpc. VLA observations of the 6 cm and 2 cm wavelength transitions provided sufficient resolution and sensitivity to resolve condensations within the foreground clouds. Solutions to the equations of statistical equilibrium within each condensation in the context of a large velocity gradient model yielded an estimate for the CMB temperature at 2.1 mm wavelength of 3.2 ± 0.9 K. The uncertainty is dominated by modeling of collisional pumping by neutral hydrogen molecules (H2). The result is the most distant measurement of the CMB to date. We discuss possible extension of the technique to systems with moderate redshift as a test of a primeval origin of the CMB.