Dynamic Adaptive Streaming over HTTP (DASH) is currently a widely adopted technology for video delivery over the Internet. DASH offers significant advantages, enabling users to switch dynamically between different available video qualities responding to variations in the current network conditions during video playback. This is particularly interesting in wireless and mobile access networks, which present unexpected and frequent such variations. Moreover, mobile users in these networks share a common radio access link and, thus, a common bottleneck in case of congestion, which may cause user experience to degrade. In this context, the Mobile Edge Computing (MEC) emerging standard gives new opportunities to improve DASH performance, by moving IT and cloud computing capabilities down to the edge of the mobile network. In this paper, we propose a novel architecture for adaptive HTTP video streaming tailored to a MEC environment. The proposed architecture includes an adaptation algorithm running as a MEC service, aiming to relax network congestion while improving user experience. Our mechanism is standards-compliant and compatible with receiver-driven adaptive video delivery algorithms, with which it cooperates in a transparent manner.