Coupled optical cavities, which support normal modes, play a critical role in optical filtering, sensing, slow-light generation, and quantum state manipulation. Recent theoretical work has proposed incorporating nonlinear materials into these systems to enable novel quantum technologies. Here, we report the first experimental demonstration of squeezing generated in a quantum-enhanced coupled-cavity system, achieving a quantum noise reduction of 3.3 dB around the normal-mode splitting frequency of 7.47 MHz. We provide a comprehensive analysis of the system's loss mechanisms and performance limitations, validating theoretical predictions. Our results underscore the promise of coupled-cavity squeezers for advanced quantum applications, including gravitational wave detection and precision sensing.