Sustainable battery concepts are of great importance for the energy storage demands of the future. Organic batteries based on redox-active polymers are one class of promising storage systems to meet these demands, in particular when combined with environmentally friendly and safe electrolytes. Deep Eutectic Solvents (DESs) represent a class of electrolytes that can be produced from sustainable sources and exhibit in most cases no or only a small environmental impact. Because of their non-flammability, DESs are safe, while providing an electrochemical stability window almost comparable to established battery electrolytes and much broader than typical aqueous electrolytes. Here, we report the first all-organic battery cell based on a DES electrolyte, which in this case is composed of sodium bis(trifluoromethanesulfonyl)imide (NaTFSI) and N-methylacetamide (NMA) alongside the electrode active materials poly(2,2,6,6-tetramethylpiperidin-1-yl-oxyl methacrylate) (PTMA) and crosslinked poly(vinylbenzylviologen) (X-PVBV$^{2+}$). The resulting cell shows two voltage plateaus at 1.07 V and 1.58 V and achieves Coulombic efficiencies of 98 %. Surprisingly, the X-PVBV/X-PVBV$^+$ redox couple turned out to be much more stable in NaTFSI : NMA 1 : 6 than the X-PVBV$^+$/X-PVBV$^{2+}$ couple, leading to asymmetric capacity fading during cycling tests.