Copper is a transition metal that plays critical roles in many life processes. Controlling the cellular concentration and trafficking of copper offers a route to disrupt these processes. Here we report small molecules that inhibit the human copper-trafficking proteins Atox1 and CCS, and so provide a selective approach to disrupt cellular copper transport. The knockdown of Atox1 and CCS or their inhibition leads to a significantly reduced proliferation of cancer cells, but not of normal cells, as well as to attenuated tumour growth in mouse models. We show that blocking copper trafficking induces cellular oxidative stress and reduces levels of cellular ATP. The reduced level of ATP results in activation of the AMP-activated protein kinase that leads to reduced lipogenesis. Both effects contribute to the inhibition of cancer cell proliferation. Our results establish copper chaperones as new targets for future developments in anticancer therapies.