  Recent experiments on kagome metals AV$_3$Sb$_5$ (A=K,Rb,Cs) [M. Kang et al.,
Nat. Phys. 18, 301-308 (2022)] identify twofold van Hove singularities (TvHS)
with opposite concavity near the Fermi energy, generating two approximately
hexagonal Fermi surfaces -- one electron-like and the other hole-like. Here we
propose that a TvHS generates a novel time-reversal symmetry breaking excitonic
order -- arising due to bound pairs of electrons and holes located at opposite
concavity van Hove singularities. We introduce a minimal model for the TvHS and
investigate interaction induced many-body instabilities via the perturbative
renormalisation group technique and a free energy analysis. Specialising to
parameters appropriate for the kagome metals AV$_3$Sb$_5$, we construct a phase
diagram comprising chiral excitons, charge density wave and a region of
coexistence. We propose this as an explanation of a diverse range of
experimental observations in AV$_3$Sb$_5$. Notably, the chiral excitonic state
gives rise to a quantum anomalous Hall conductance, providing an appealing
interpretation of the observed anomalous Hall effect in kagome metals. Possible
alternative realisations of the TvHS mechanism in bilayer materials are also
discussed. We suggest that TvHS open up interesting possibilities for
correlated phases, enriching the set of competing ground states to include
excitonic order.
