We consider the dissolution of a chemically inert solid in a binary liquid mixture with a critical point of solution. When the mixture, acting as the solvent, has come to equilibrium with the solid, the state of the system is completely described by the temperature, pressure, and a concentration variable formed by dividing the molar amount of one solvent component by that of the other. Under conditions of fixed pressure, the principle of critical point isomorphism predicts that the slope of a van't Hoff plot of the solubility of the solid should diverge toward infinity as the temperature enters the critical region. The sign of the divergence is negative when the dissolution is endothermic, whereas it is positive when the dissolution is exothermic. In experiments where excess solid phenolphthalein dissolves in a binary mixture of nitrobenzene + dodecane, we have observed exothermic dissolution concurrently with a positive divergence of the van't Hoff slope. The data are insufficiently precise to compute an accurate numerical value for the exponent of the temperature power law expected to govern this divergence; nevertheless, on the basis of Widom scaling theory, we argue that the exponent should be equal to 0.326, which is identical to the value of the exponent that governs the temperature dependence of the shape of the liquid-liquid coexistence curve. Being entirely physical in nature, the anomalous solubility effect should be observable in the case of any chemically inert solid dissolving in any one of the more than 1000 liquid pairs known to have a critical point of solution.