The invention provides for a write-once nonvolatile memory array, the memory cells comprising a phase change material, such as a chalcogenide. Phase change is achieved in chalcogenide memories by thermal means. The initial, unprogrammed state of each memory cell is a crystalline, low-resistance state, while the programmed state is an amorphous, high-resistance state. Optimizing the circuitry for a write-only memory array, the wordlines or bitlines can be long, with at least 256 cells on a wordline or bitline, and in some embodiments, having thousands of cells on a wordline or bitline. In a preferred embodiment, such an array can be a monolithic three dimensional memory array comprising stacked memory levels.