Networks increasingly incorporate complex functionality, going beyond simple forwarding. Packet flows require processing through a complex set of services, that may often be provided in the cloud or on commercial off the shelf (COTS) hardware. This paper investigates the problem of scheduling network functions in different service chains, on a single physical host. Stock operating system (OS) schedulers are ill-equipped to handle the strict performance required - high throughput AND low latency across multiple functions - by network function virtualization (NFV) platforms. Our experimental results show that the standard Linux scheduler can cause a 50% drop in throughput when subjected to diverse NFV workloads. We argue that the OS scheduler needs to be enhanced to be NFV-aware in order to handle service chains, while maintaining line-rate performance. We describe the challenges in designing a network function service chain friendly scheduler and present some early results based on our ongoing research in this area.