The scale of data and the demand for high data rates in applications are rapidly increasing over the years. By moving the computing resources closer to the users, edge computing minimizes the latency caused by otherwise pulling the data between the user and a centralized platform. Thus, data centers and computing nodes at the edge continue to overtake or replace traditional centralized cloud platforms in various 5G applications and use cases. Network functions virtualization virtualizes dedicated hardware network middleboxes into virtual network functions (VNFs) and deploys them on top of servers and data centers. Due to the inherent bandwidth cost associated with the distance between the network services and the end user, more and more third‐party VNF providers choose to deploy their services at the edge, rather than in a centralized cloud. A typical network service chaining (NSC) consumes various network services, where one's output becomes the input of another. As network services are often latency sensitive, NSC needs to be carried out, maintaining proximity to the user as well as among the services composing the NSC. In this paper, we present the design of a resilient and adaptive framework, following an approach inspired by software‐defined networking, for the remote users to construct network service chains in the mobile and edge computing environments. Our evaluations highlight the efficiency and optimality of the framework in finding the best fit among several third‐party edge VNFs in deploying the user network service chains, abiding by various user policies.