We present ChronOS Linux, a best-effort real-time Linux kernel for chip multiprocessors (CMPs). ChronOS addresses the intersection of three problem spaces: a) OS-support for obtaining best-effort timing assurances, b) real-time Linux kernel augmented with the PREEMPT_RT patch, and c) OS support for CMP-aware real-time scheduling. While each of these spaces have been studied in the past, their intersection, which has strong problem motivations, was previously empty. Best-effort timeliness targets real-time applications with run-time uncertainties and resource overloads, and optimizes collective application timeliness --- as specified by the application. ChronOS directly supports the implementation of best-effort real-time schedulers on CMPs, in addition to others, in the global and partitioned scheduling disciplines. ChronOS extends the PREEMPT_RT Linux patch, and thus provides full kernel preemptibility and retains stock Linux features. We validate our claims by reporting on the implementation of a suite of best-effort and non-best-effort CMP schedulers on a quad-core AMD Phenom platform.