Programs written in C/C++ can suffer from serious memory fragmentation, leading to low utilization of memory, degraded performance, and application failure due to memory exhaustion. This paper introduces Mesh, a plug-in replacement for malloc that, for the first time, eliminates fragmentation in unmodified C/C++ applications. Mesh combines novel randomized algorithms with widely-supported virtual memory operations to provably reduce fragmentation, breaking the classical Robson bounds with high probability. Mesh generally matches the runtime performance of state-of-the-art memory allocators while reducing memory consumption; in particular, it reduces the memory of consumption of Firefox by 16% and Redis by 39%.