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[Abridged] Observations of molecular gas at all redshifts are critical formeasuring the cosmic evolution in molecular gas density and understanding thestar-formation history of the Universe. The 12CO molecule (J=1-0 transition =115.27 GHz) is the best proxy for extragalactic H2, which is the gas reservoirfrom which star formation occurs, and has been detected out to z~6. Typically,redshifted high-J lines are observed at mm-wavelengths, the most commonlytargeted systems exhibiting high SFRs (e.g. submm galaxies), and far-IR-brightQSOs. While the most luminous objects are the most readily observed, detectionsof more typical galaxies with modest SFRs are essential for completing thepicture. ALMA will be revolutionary in terms of increasing the detection rateand pushing the sensitivity limit down to include such galaxies, however thelimited FoV when observing at such high frequencies makes it difficult to useALMA for studies of the large-scale structure traced out by molecular gas ingalaxies. This article introduces a strategy for a systematic search formolecular gas during the EoR (z~7 and above), capitalizing on the fact that theJ=1-0 transition of 12CO enters the upper bands of cm-wave instruments athigh-z. The FoV advantage gained by observing at such frequencies, coupled withmodern broadband correlators allows significant cosmological volumes to beprobed on reasonable timescales. In this article we present an overview of ourfuture observing programme which has been awarded 6,500 hours as one of theLarge Survey Projects for MeerKAT, the forthcoming South African SKA pathfinderinstrument. Its large FoV and correlator bandwidth, and high-sensitivityprovide unprecedented survey speed for such work. An existing astrophysicalsimulation is coupled with instrumental considerations to demonstrate thefeasibility of such observations and predict detection rates.

MESMER: MeerKAT Search for Molecules in the Epoch of Reionization