Network function virtualization (NFV) provides the flexibility for service providers to scale up their service systems and also enhances the possibility to satisfy user demand with limited resources by enabling network functions on commodity servers, as well as by allowing multiple identical network functions existing in the service networks. On the other hand, to accommodate various user demands, multiple service chains need to be applied in this network. However, due to the flow mingling problem in network service chaining, the system throughput can hardly be evaluated, and determining multiple service chains becomes a challenge. In this work, we identify two types of flow-mingling problems: intra-chains link contention and inter-chains link contention, and propose an algorithm named NACHOS to facilitate selection of multiple service chains. As a result, NACHOS can result in the optimality with maximum available bandwidth in a datacenter network, and can select service chains in polynomial time.