This paper presents a fundamental law for parallel performance: it shows that parallel performance is not only limited by sequential code (as suggested by Amdahls law) but is also fundamentally limited by synchronization through critical sections. Extending Amdahls software model to include critical sections, we derive the surprising result that the impact of critical sections on parallel performance can be modeled as a completely sequential part and a completely parallel part. The sequential part is determined by the probability for entering a critical section and the contention probability (i.e., multiple threads wanting to enter the same critical section). This fundamental result reveals at least three important insights for multicore design. (i) Asymmetric multicore processors deliver less performance benefits relative to symmetric processors than suggested by Amdahls law, and in some cases even worse performance. (ii) Amdahls law suggests many tiny cores for optimum performance in asymmetric processors, however, we find that fewer but larger small cores can yield substantially better performance. (iii) Executing critical sections on the big core can yield substantial speedups, however, performance is sensitive to the accuracy of the critical section contention predictor.