The fifth generation (5G) mobile communication network aims at providing high-rate, low-latency services. When a user subscribes a chain of service functions (a.k.a. service chain) from the telecom providers, a Service Level Agreement (SLA) is specified according to his requirement. Deploying service chains optimally has always been a big issue. Several previous works have presented various strategies of service-chain deployment for optimizing either latency or computational resources; however, over-optimization of latency or computational resource is not necessarily equivalent to improvement on quality of experience. Therefore, in this paper, we formally formulate this problem of optimizing quality of experience with the queuing theory and mixed-integer linear programming. In addition, we propose an efficient algorithm named 'QoE-driven Service-Chain Deployment with Latency Prediction' for deploying a service chain for a user in practice. According to the experiments, our algorithm reduces > 99% rejections and > 99% waiting time, notably elevating the quality of experience for users.