  Carbon-14 ($^{14}$C) is produced in the atmosphere when neutrons from
cosmic-ray air showers are captured by $^{14}$N nuclei. Atmospheric $^{14}$C
becomes trapped in air bubbles in polar ice as compacted snow (firn) transforms
into ice. $^{14}$C is also produced in situ in ice grains by penetrating
cosmic-ray neutrons and muons. Recent ice core measurements indicate that in
the $^{14}$CO phase, the $^{14}$C is dominated by the in situ cosmogenic
component at most ice coring sites. Thus, it should be possible to use
ice-bound $^{14}$CO to reconstruct the historical flux of cosmic rays at Earth,
without the transport and deposition uncertainties associated with $^{10}$Be or
the carbon cycle uncertainties affecting atmospheric $^{14}$CO$_2$. The
measurements will be sensitive to the cosmic-ray flux above the energy range
most affected by solar modulation. We present estimates of the expected
sensitivity of $^{14}$CO in ice cores to the historical flux of Galactic cosmic
rays, based on recent studies of $^{14}$CO in polar ice.
