With the unprecedented development of smart mobile devices (SMDs), e.g., Internet-of-Things devices and smartphones, various computation-intensive applications are explosively increasing in ultradense networks (UDNs). Mobile-edge computing (MEC) has emerged as a key technology to alleviate the computation workloads of SMDs and decrease service latency for computation-intensive applications. With the benefits of network function virtualization, MEC can be integrated with the cloud radio access network (C-RAN) in UDNs for computation and communication cooperation. However, with stochastic computation task arrivals and time-varying channel states, it is challenging to offload computation tasks online with energy-efficient computation and radio resource management. In this article, we investigate the task offloading and resource allocation problem in MEC-enabled dense C-RAN, aiming at optimizing network energy efficiency. A stochastic mixed-integer nonlinear programming problem is formulated to jointly optimize the task offloading decision, elastic computation resource scheduling, and radio resource allocation. To tackle the problem, the Lyapunov optimization theory is introduced to decompose the original problem into four individual subproblems which are solved by convex decomposition methods and matching game. We theoretically analyze the tradeoff between energy efficiency and service delay. Extensive simulations evaluate the impacts of system parameters on both energy efficiency and service delay. The simulation results also validate the superiority of the proposed task offloading and resource allocation scheme in dense C-RAN.