  In this work we provide a link between a nearly vanishing cosmological
constant and chiral symmetry. This is accomplished with a modification of
General Relativity coupled to a topological field theory, namely BF theory by
introducing fermions charged under the BF theory gauge group. We find that the
cosmological constant sources a chiral anomaly for the fermions, providing a
`technical naturalness' explanation for the smallness of the observed
cosmological constant. Applied to the early universe, we show that production
of fermions during inflation can provide all the dark matter in the universe
today, in the form of superheavy dark baryons.
