Chip Multiprocessors (CMPs) are flexible, high-frequency platforms on which to support Thread-Level Speculation (TLS). However, for TLS to deliver on its promise, CMPs must exploit multiple sources of speculative task-level parallelism, including any nesting levels of both subroutines and loop iterations. Unfortunately, these environments are hard to support in decentralized CMP hardware: since tasks are spawned out-of-order and unpredictably, maintaining key TLS basics such as task ordering and efficient resource allocation is challenging. While the concept of out-of-order spawning is not new, this paper is the first to propose a set of microarchitectural mechanisms that, altogether, fundamentally enable fast TLS with out-of-order spawn in a CMP. Moreover, we develop a fully-automated TLS compiler for aggressive out-of-order spawn. With our mechanisms, a TLS CMP with