Network Function Virtualization (NFV) has gained a significant research interest in both academia and industry since its inception in the late 2012. One of the key research issues in NFV is the development of systems for building Virtual Network Functions (VNFs) capable of meeting the erformance requirements of enterprise and telecommunication networks. New packet processing models leveraging kernel bypass I/O and poll-mode processing have gained popularity for building high performance VNFs because of their simple programming model and very low I/O overhead. However, a major drawback of such poll-mode processing is the inefficient use of CPU resources. Existing CPU schedulers are ill-suited for VNFs due to their inability to capture the actual processing cost of a poll-mode VNF, hence, cannot rightsize the CPU allocation. This is further exacerbated by their inability to consider VNF processing order when VNFs are chained to form Service Function Chains (SFCs). The state-of-the-art solutions proposed for VNF scheduling are intrusive, i.e., requiring the VNFs to be built with scheduler specific libraries or having carefully selected scheduling checkpoints. This highly restricts the VNFs that can properly work with such schedulers. In this paper, we present UNiS: a User-space Non-intrusive work-flow aware VNF Scheduler. Unlike existing approaches, UNiS does not require VNF modifications and treats the poll-mode VNFs as a black box, hence, is non-intrusive. UNiS is also workflow-aware, i.e., maintains SFC processing order while scheduling the VNFs. Testbed experiments show that UNiS is able to achieve a throughput within 90% (for synthetic traffic load) and 98% (for real data center traffic trace) of the achievable throughput using an intrusive co-operative scheduler.