The Kondo singlet—a many-body state formed by entanglement between a localized spin and the Fermi sea—has been studied extensively through its transport signatures in quantum dots. Here we report a thermodynamic measurement of the entropy suppression associated with the formation of the Kondo singlet, using temperature-dependent charge sensing and a Maxwell relation to track the suppression of spin entropy as the first electron is added to a strongly-coupled GaAs quantum dot. Plotting dN/dT against the simultaneously measured occupation N reveals an asymmetric lineshape with its peak shifted to N>1/2---a hallmark of Kondo screening—that weakens with increasing temperature and is qualitatively reproduced by numerical renormalization group (NRG) calculations, with a small but persistent offset to lower occupation relative to the theory. An independent measurement of conductance versus occupation on the same device provides a test of these quantities through the mixed-valence crossover and matches NRG within experimental uncertainty.