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Abstract: We show that the ground state of a weakly charged two-dimensional electron-hole fluid in a strong magnetic field is a broken translation symmetry state with interpenetrating lattices of localized vortices and antivortices in the electron-hole-pair field. The vortices and antivortices carry fractional charges of equal sign but unequal magnitude and have a honeycomb-lattice structure that contrasts with the triangular lattices of superconducting electron-electron-pair vortex lattices. We predict that increasing charge density or a weakening magnetic field drives a vortex delocalization transition that would be signaled experimentally by an abrupt increase in counterflow transport resistance.