  We quantify the prospects for using emission lines from rotational
transitions of the CO molecule to perform an `intensity mapping' observation at
high redshift during the Epoch of Reionization (EoR). The aim of CO intensity
mapping is to observe the combined CO emission from many unresolved galaxies,
to measure the spatial fluctuations in this emission, and use this as a tracer
of large scale structure at very early times in the history of our Universe.
This measurement would help determine the properties of molecular clouds -- the
sites of star formation -- in the very galaxies that reionize the Universe. We
further consider the possibility of cross-correlating CO intensity maps with
future observations of the redshifted 21 cm line. The cross spectrum is less
sensitive to foreground contamination than the auto power spectra, and can
therefore help confirm the high redshift origin of each signal. Furthermore,
the cross spectrum measurement would help extract key information about the
EoR, especially regarding the size distribution of ionized regions. We discuss
uncertainties in predicting the CO signal at high redshift, and discuss
strategies for improving these predictions. Under favorable assumptions, and
feasible specifications for a CO survey mapping the CO(2-1) and CO(1-0) lines,
the power spectrum of CO emission fluctuations and its cross spectrum with
future 21 cm measurements from the MWA are detectable at high significance.

Cosmology and Nongalactic Astrophysics