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Major microprocessor vendors have integrated functional software-based self-testing in their manufacturing test flows during the last decade. Functional self-testing is performed by test programs that the processor executes at-speed from on-chip memory. Multiprocessors and multithreaded architectures are constantly becoming the typical general-purpose computing paradigm, and thus the various existing uniprocessor functional self-testing schemes must be adopted and adjusted to meet the testing requirements of complex multiprocessors. A major challenge in porting a functional self-testing approach from the uniprocessor to the multiprocessor case is to take advantage of the inherent execution parallelism offered by the multiple cores and the multiple threads in order to reduce test execution time. In this paper, we study the application of functional self-testing to chip multithreaded (CMT) processors. We propose a method that exploits thread-level parallelism (TLP) to speed up the execution of self-test routines in every physical core of a multiprocessor chip. The proposed method effectively splits the self-test routines into shorter ones, assigns the new routines to the hardware threads of the core and schedules their execution in order to minimize the core idle intervals due to cache misses or long latency operations and maximize the utilization of core computing resources. We demonstrate our method in the open-source CMT multiprocessor model, Sunpsilas OpenSPARC T1, which contains eight CPU cores, each one supporting four hardware threads. Our experimental results show a self-test execution speedup of more than three times compared to the single thread execution.