Recycling of the carbon atoms from plastic waste is a crucial step in establishing a circular economy. The intense sorting required to produce easily treatable streams inevitably produces highly heterogeneous waste byproducts, which are challenging to recycle. In this paper, we propose that automotive shredder residue (ASR), which is one such heterogeneous waste, can be recycled by chemical-looping gasification (CLG), using its own ash as the oxygen-carrying bed material. We investigate two critical issues regarding the feasibility of the process: how to achieve complete conversion of the ASR in the fuel reactor and whether the heat of oxidation of the bed material is sufficient to fulfill the energy demand of the process, especially when complete conversion of ASR is achieved in the fuel reactor. This work is based on experiments conducted in the 2–4 MWth Chalmers dual fluidized bed gasifier. Assessed were the impacts on ASR conversion of four operational parameters: the bed material circulation rate; the ASR feeding rate; the levels of oxygen transport between the reactors; and the fuel reactor temperature. A heat balance for the system was established to assess the feasibility of CLG from the energy standpoint. The transport of oxygen was found to be the decisive parameter in the process, as it had the strongest impact on ASR conversion and directly affected the heat release in the air reactor. The oxygen transport level was found to be insufficient to cover the heat demand of the CLG process, indicating that strategies to increase oxygen transport are needed. However, carbon dioxide was found to be the main product of the process (on a carbon basis) and the carbon that was converted by increasing the oxygen transport formed carbon dioxide exclusively. Therefore, the viability of the CLG process for ASR recycling requires the valorization of carbon dioxide.