  We propose a vortex Chern insulator, motivated by recent experimental
demonstrations on programmable arrangements of cavity polariton vortices by
[Alyatkin et al., ArXiv:2207.01850 (2022)] and [Wang et al., National Sci. Rev.
10, Nwac096 (2022)]. In the absence of any external fields, time-reversal
symmetry is spontaneously broken through polariton condensation into structured
arrangements of localized co-rotating vortices. We characterize the response of
the rotating condensate lattice by calculating the spectrum of Bogoliubov
elementary excitations and observe the crossing of edge-states, of opposite
vorticity, connecting bands with opposite Chern numbers. The emergent
topologically nontrivial energy gap stems from inherent vortex anisotropic
polariton-polariton interactions and does not require any spin-orbit coupling,
external magnetic fields, or elliptically polarized pump fields.
