The supersolid phase is a self-organized state of matter that simultaneously exhibits the crystalline order of a solid and the frictionless flow of a superfluid. Its formation requires the simultaneous breaking of phase and translational symmetries—a stringent condition that makes experimental observation challenging. Here we show that it is possible to achieve a room-temperature supersolid phase by integrating single-crystal halide perovskites with an exciton–polariton nanograting. This architecture supports a hybrid polaritonic bound-state-in-continuum state with a large bandgap (18.2 meV) and two side modes. As the pumping intensity increases, optical parametric oscillation drives the system from a bound-state-in-continuum polariton condensate into the two side modes, forming a self-organized supersolid phase characterized by a striped one-dimensional lattice spanning the condensate. Crucially, single-shot real-space imaging shows stochastic phase selection of the stripe pattern, evidenced by strong suppression of the density modulation on multishot averaging. The observation of supersolidity is further supported by long-range spatiotemporal coherence measured interferometrically and by a non-rigid supersolid lattice. The realization of supersolidity at room temperature in a polaritonic nanograting platform can be useful to control exotic quantum orders and for exploring spontaneous symmetry breaking, quantum coherence and collective excitations in driven quantum materials.