  We discuss how measurements of fluctuations in the absorption of cosmic
microwave background (CMB) photons by neutral gas during the cosmic dark ages,
at redshifts z ~ 7--200, could reveal the primordial deuterium abundance of the
Universe. The strength of the cross-correlation of brightness-temperature
fluctuations due to resonant absorption of CMB photons in the 21-cm line of
neutral hydrogen with those due to resonant absorption of CMB photons in the
92-cm line of neutral deuterium is proportional to the fossil deuterium to
hydrogen ratio [D/H] fixed during big bang nucleosynthesis (BBN). Although
technically challenging, this measurement could provide the cleanest possible
determination of [D/H], free from contamination by structure formation
processes at lower redshifts, and has the potential to improve BBN constraints
to the baryon density of the Universe \Omega_{b} h^2. We also present our
results for the thermal spin-change cross-section for deuterium-hydrogen
scattering, which may be useful in a more general context than we describe
here.
