An elegantly simple and probably ancient molecular mechanism of allostery is described for the Escherichia coli arginine repressor ArgR, the master feedback regulator of transcription in L-arginine metabolism. Molecular dynamics simulations with ArgRC, the hexameric domain that binds L-arginine with negative cooperativity, reveal that conserved arginine and aspartate residues in each ligand-binding pocket promote rotational oscillation of apoArgRC trimers by engagement and release of hydrogen-bonded salt bridges. Binding of exogenous L-arginine displaces resident arginine residues and arrests oscillation, shifting the equilibrium quaternary ensemble and promoting motions that maintain the configurational entropy of the system. A single L-arg ligand is necessary and sufficient to arrest oscillation, and enables formation of a cooperative hydrogen-bond network at the subunit interface. The results are used to construct a free-energy reaction coordinate that accounts for the negative cooperativity and distinctive thermodynamic signature of L-arginine binding detected by calorimetry. The symmetry of the hexamer is maintained as each ligand binds, despite the conceptual asymmetry of partially-liganded states. The results thus offer the first opportunity to describe in structural and thermodynamic terms the symmetric relaxed state predicted by the concerted allostery model of Monod, Wyman, and Changeux, revealing that this state is achieved by exploiting the dynamics of the assembly and the distributed nature of its cohesive free energy. The ArgR example reveals that symmetry can be maintained even when binding sites fill sequentially due to negative cooperativity, which was not anticipated by the Monod, Wyman, and Changeux model. The molecular mechanism identified here neither specifies nor requires a pathway for transmission of the allosteric signal through the protein, and it suggests the possibility that binding of free amino acids was an early innovation in the evolution of allostery.