Traditional networks employ expensive dedicated hardware devices as middleboxes to implement Service Chains (SC) of user requests by steering data traffic along the middleboxes in the service chains. Network Function Virtualization (NFV) is a promising virtualization technique by implementing network functions as pieces of software in servers or data centers. By leveraging the technique of Software Defined Networking (SDN), NFV can be further enabled in a flexible and dynamic way. In this paper, we consider dynamic admissions of delay-aware NFV-enabled requests in SDNs by leveraging pre-installed NFV instances in data centers. We first formulate a novel revenue maximization problem, and show that the problem is NP-hard. We then propose an online heuristic for the problem. We also devise an online algorithm with a provable competitive ratio for a special case of the problem where the end-to-end delay requirement of requests can be neglected. We finally evaluate the performance of the proposed algorithms through experimental simulations. The simulation results demonstrate that the proposed algorithms are promising.