We present a new method — Speculative Lock Reordering (SLR) — that enables multiple threads to concurrently and speculatively execute within a critical section. Its novel feature is to exploit that there is no a priori execution order between separate invocations of a critical section that speculatively executed threads must respect. In contrast to previously proposed speculative synchronization schemes, we show that since an execution order can be selected that removes as many data dependences as possible, SLR can expose more concurrency. Additionally, it is shown that SLR can be implemented in a chip-multiprocessor by only modest extensions to already published thread-level data dependence speculation systems.