0_8023 A supersolid, a counter-intuitive quantum state in which a rigid lattice of particles flows without resistance, has to date not been unambiguously realized.  Here we reveal a supersolid ground state of excitons, formed from spatially separated electrons and holes in a  semiconductor heterostructure.  The supersolid is driven by a large exciton dipole moment and occurs at electron-hole separations lying outside the focus of recent transport experiments on exciton superfluidity in double layer systems [1].  Our supersolid conforms to the original Chester concept of a supersolid [2] with one exciton per supersolid site.  It is distinct from an alternative version observed in cold-atom systems which is characterized by a cluster of condensates [3].  In the phase diagram, the new supersolid phase appears at electron-hole separations much smaller than for the predicted exciton normal solid [4], and it persists up to a solid-solid transition where the quantum phase coherence collapses while leaving the translational symmetry preserved.  The ranges of electron-hole separations and exciton densities in our phase diagram are well within reach of current experimental capabilities.[1] Z. Wang, et al., Nature 574, 76 (2019); L. Ma, et al., Nature 598, 585(2021)
[2] G. V. Chester, Phys. Rev. A 2 256 (1970)
[3] M. A. Norcia, et al., Nature 596, 375 (2021)
[4] G. E. Astrakharchik, J. Boronat, I. L. Kurbakov, and Yu. E. Lozovik, Phys. Rev. Lett. 98, 060405 (2007)