  The redshifted 21-cm emission by neutral hydrogen offers a unique tool for
mapping structure formation in the early universe in three dimensions. Here we
provide the first detailed calculation of the 21-cm emission signal during and
after the epoch of hydrogen recombination in the redshift range of z ~
500-1,100, corresponding to observed wavelengths of 100-230 meters. The 21-cm
line deviates from thermal equilibrium with the cosmic microwave background
(CMB) due to the excess Ly-alpha radiation from hydrogen and helium
recombinations. The resulting 21-cm signal reaches a brightness temperature of
a milli-Kelvin, orders of magnitude larger than previously estimated. Its
detection by a future lunar or space-based observatory could improve
dramatically the statistical constraints on the cosmological initial conditions
compared to existing two-dimensional maps of the CMB anisotropies.
