The chiral anomaly is the predicted breakdown of chiral symmetry in a Weyl semimetal with monopoles of opposite chirality when an electric field is applied parallel to a magnetic field. It occurs because of charge pumping between monopoles of opposite chirality. Experimental observation of this fundamental effect is plagued by concerns about the current pathways. Here we demonstrate the thermal chiral anomaly, energy pumping between monopoles, in topological insulator bismuth–antimony alloys driven into an ideal Weyl semimetal state by a Zeeman field, with the chemical potential pinned at the Weyl points and in the absence of any trivial Fermi surface pockets. The experimental signature is a large enhancement of the thermal conductivity in an applied magnetic field parallel to the thermal gradient. This work demonstrates both pumping of energy and charge between the two Weyl points of opposite chirality and that they are related by the Wiedemann–Franz law.