A valence critical end point existing near the absolute zero provides a unique case for the study of a quantum version of the strong density fluctuation at the Widom line in the supercritical fluids. Although singular charge and orbital dynamics are suggested theoretically to alter the electronic structure significantly, breaking down the standard quasi-particle picture, this has never been confirmed experimentally to date. We provide the first empirical evidence that the proximity to quantum valence criticality leads to a clear breakdown of Fermi liquid behavior. Our detailed study of the mixed valence compound α-YbAlB4 reveals that a small chemical substitution induces a sharp valence crossover, accompanied by a pronounced non-Fermi liquid behavior characterized by a divergent effective mass and unusual T/B scaling in the magnetization.