This paper introduces an information-entropy correction to the circular restricted three-body problem (CR3BP) using the Kilgore Field Equation (KFE), a nonlinear coupling that modifies the effective potential or adds a weak feedback force. By integrating Earth–Moon–type libration orbits around L₄, we show that small positive observer-coupling parameters reduce local chaotic sensitivity, tighten invariant tori, and induce only minimal, controlled Jacobi-energy drift. All effects vanish smoothly as the coupling parameters go to zero, recovering the standard CR3BP. This work provides the first demonstration that an explicitly information-theoretic regularization can soften chaotic transport in a gravitational three-body system without breaking its structure.