One embodiment of the present invention provides a system that enforces memory reference ordering requirements, such as Total Store Ordering (TSO), at a Level 1 (L1) cache in a multiprocessor. During operation, while executing instructions in a speculative-execution mode, the system receives an invalidation signal for a cache line at the L1 cache wherein the invalidation signal is received from a cache-coherence system within the multiprocessor. In response to the invalidation signal, if the cache line exists in the L1 cache, the system examines a load-mark in the cache line, wherein the load-mark being set indicates that the cache line has been loaded from during speculative execution. If the load-mark is set, the system fails the speculative-execution mode and resumes a normal-execution mode from a checkpoint. By failing the speculative-execution mode, the system ensures that a potential update to the cache line indicated by the invalidation signal will not cause the memory reference ordering requirements to be violated during the speculative-execution mode.