While hardware is evolving toward heterogeneous multicore architectures, modern software applications are increasingly written in managed languages. Heterogeneity was born of a need to improve energy efficiency; however, we want the performance of our applications not to suffer from limited resources. How best to schedule managed language applications on a mix of big, out-of-order cores and small, in-order cores is an open question, complicated by the host of service threads that perform key tasks such as memory management. These service threads compete with the application for core and memory resources, and garbage collection (GC) must sometimes suspend the application if there is not enough memory available for allocation. In this article, we explore concurrent garbage collection?s behavior, particularly when it becomes critical, and how to schedule it on a heterogeneous system to optimize application performance. While some applications see no difference in performance when GC threads are run on big versus small cores, others?those with GC criticality?see up to an 18% performance improvement. We develop a new, adaptive scheduling algorithm that responds to GC criticality signals from the managed runtime, giving more big-core cycles to the concurrent collector when it is under pressure and in danger of suspending the application. Our experimental results show that our GC-criticality-aware scheduler is robust across a range of heterogeneous architectures with different core counts and frequency scaling and across heap sizes. Our algorithm is performance and energy neutral for GC-uncritical Java applications and significantly speeds up GC-critical applications by 16%, on average, while being 20% more energy efficient for a heterogeneous multicore with three big cores and one small core.