This paper presents the Mitosis framework, which is a combined hardware-software approach to speculative multithreading, even in the presence of frequent dependences among threads. Speculative multithreading increases single-threaded application performance by exploiting thread-level parallelism speculatively - that is, executing code in parallel even when the compiler or runtime system cannot guarantee the parallelism exists. The proposed approach is based on predicting/computing thread input values via software, through a piece of code that is added at the beginning of each thread (the pre-computation slice). A pre-computation slice is expected to compute the correct thread input values most of the time, but not necessarily always. This allows aggressive optimization techniques to be applied to the slice to make it very short. This paper focuses on the microarchitecture that supports this execution model. The primary novelty of the microarchitecture is the hardware support for the execution and validation of pre-computation slices. Additionally, this paper presents new architectures for the register file and the cache memory in order to support multiple versions of each variable and allow for efficient roll-back in case of misspeculation. We show that the proposed microarchitecture, together with the compiler support, achieves an average speedup of 2.2 for applications that conventional non-speculative approaches are not able to parallelize at all.