In patients with Wilson’s disease, the deficiency of the copper carrier ATP7B causes the accumulation of copper in the liver, brain and various other organs. Lifelong treatment is therefore mandatory, using copper chelators to increase the excretion of copper and to avoid life-threatening damage. The clinically used reference drug, D-penicillamine, exhibit numerous adverse effects, especially a frequent severe and irreversible neurological worsening, mainly due to its lack of metal selectivity; (2) Methods: A new tetradentate ligand based on an 8-aminoquinoline entity, named TDMQ20, which is highly selective for copper compared with other metal ions, is evaluated in “toxic milk” TX mice as an oral treatment of this Wilson’s disease murine model; (3) Results: The concentration of copper in the liver of “toxic milk” TX mice decreased and the fecal excretion of copper increased upon oral treatment with TDMQ20. Both effects are dose-dependent, and more pronounced than those of D-penicillamine; (4) Conclusions: The TDMQ20 copper chelator is more efficient than the reference drug D-penicillamine for the treatment of a Wilson’s disease murine model. Pharmacological data obtained with TDMQ20 on the TX mouse model strongly support the selection of this ligand as a drug candidate for this genetic disease.