  We consider the potential for line intensity mapping (IM) experiments to
measure the baryon acoustic oscillations (BAO) from 3 < z < 6. This would
constrain the expansion history in a redshift range that is currently
unexplored. We calculate the map depths that future IM experiments targeting
the CO(1-0) rotational transition line and [CII] ionized carbon fine-structure
line would need to achieve in order to measure the BAO. We find that
near-future IM experiments could constrain the BAO scale to 5% or better
depending on CO/[CII] model amplitude. This measurement is at a precision that
could make competitive constraints on models of early dark energy.
