In C, the order of evaluation of expressions is unspecified; further for expressions that do not involve function calls, C semantics ensure that there cannot be a data race between two evaluations that can proceed in either order (or concurrently). We explore the optimization opportunity enabled by these non-deterministic expression evaluation semantics in C, and provide a sound compile-time alias analysis to realize this opportunity. Our alias analysis algorithm is implemented in a tool called OOElala as a part of the Clang/LLVM infrastructure. Our experimental results demonstrate that the untapped optimization opportunity is significant: code patterns that enable such optimizations are common; the enabled transformations can range from vectorization to improved instruction selection and register allocation; and the resulting speedups can be as high as 2.6x on already-optimized real-world code.