We explore the exciton-polariton condensation in two degenerate orbital states. In the honeycomb lattice potential, at the third band we have two degenerate vortex-antivortex lattice states at inequivalent K- and K'-points. We have observed energetically degenerate condensates within the linewidth similar to 0.3 meV, and directly measured the vortex-antivortex lattice phase order of the order parameter. We have also observed the intensity anticorrelation between polariton condensates at the K- and K'-points. We relate this intensity anticorrelation to the dynamical feature of polariton condensates induced by the stochastic relaxation from the common particle reservoir.