  Distortions of the observed cosmic microwave background imprinted by the
Sunyaev-Zel'dovich effect toward massive galaxy clusters due to inverse Compton
scattering of microwave photons by high-energy electrons provide a direct
measurement of the microwave background temperature at redshifts from 0 to 1.
Some additional background temperature estimates exist at redshifts from 1.8 to
3.3 based on molecular and atomic line excitation temperatures in quasar
absorption line systems, but are model dependent. To date, no deviations from
the expected (1+z) scaling behavior of the microwave background temperature
have been seen, but the measurements have not extended deeply into the
matter-dominated era of the universe at redshifts z>3.3. Here we report the
detection of sub-millimeter line absorption from the water molecule against the
cosmic microwave background at z=6.34 in a massive starburst galaxy,
corresponding to a lookback time of 12.8 Gyr. Radiative pumping of the upper
level of the ground-state ortho-H2O(110-101) line due to starburst activity in
the dusty galaxy HFLS3 results in a cooling to below the redshifted microwave
background temperature, after the transition is initially excited by the
microwave background. The strength of this effect implies a microwave
background temperature of 16.4-30.2 K (1-sigma range) at z=6.34, which is
consistent with a background temperature increase with redshift as expected
from the standard CDM cosmology.
