HTTP Adaptive Streaming (HAS) is quickly becoming the de facto standard for video streaming services. In HAS, each video is temporally segmented and stored in different quality levels. Rate adaptation heuristics, deployed at the video player, allow the most appropriate level to be dynamically requested, based on the current network conditions. It has been shown that today's heuristics underperform when multiple clients consume video at the same time, due to fairness issues among clients. Concretely, this means that different clients negatively influence each other as they compete for shared network resources. In this article, we propose a novel rate adaptation algorithm called FINEAS (Fair In-Network Enhanced Adaptive Streaming), capable of increasing clients' Quality of Experience (QoE) and achieving fairness in a multiclient setting. A key element of this approach is an in-network system of coordination proxies in charge of facilitating fair resource sharing among clients. The strength of this approach is threefold. First, fairness is achieved without explicit communication among clients and thus no significant overhead is introduced into the network. Second, the system of coordination proxies is transparent to the clients, that is, the clients do not need to be aware of its presence. Third, the HAS principle is maintained, as the in-network components only provide the clients with new information and suggestions, while the rate adaptation decision remains the sole responsibility of the clients themselves. We evaluate this novel approach through simulations, under highly variable bandwidth conditions and in several multiclient scenarios. We show how the proposed approach can improve fairness up to 80% compared to state-of-the-art HAS heuristics in a scenario with three networks, each containing 30 clients streaming video at the same time. Latré, Middelheimlaan 1, B-2020 Antwerp, Belgium; emails: {jeroen.famaey, steven.latre}@uantwerpen.be. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee.