Due to the dynamic, slowly time-varying, and strongly nonlinear characteristics of lithium-ion batteries in use, identifying the unknown parameters of first-order RC models online faces challenges, such as low accuracy and poor real-time performance. To address this issue, a chaotic system is proposed based on a charge-controlled memristor and a first-order RC model. The charge-controlled memristor parameters are adjusted to drive the system into a chaotic state, and the system’s dynamic characteristics are analyzed. Next, an adaptive control law of the unknown parameters of the chaotic system is constructed and applied to the chaotic system. This enables the online identification of unknown parameters of the first-order RC model of lithium batteries in real time, obtaining effective parameter values and overcoming shortcomings of traditional estimation algorithms that are limited by the size of data sample space and affected by factors such as ambient temperature, road conditions, load conditions, and battery materials. The experimental simulation results show that the chaotic system established in this paper possesses rich dynamic characteristics, and the proposed adaptive control algorithm for unknown parameter identification offers good real-time performance, accuracy, robustness, and fast convergence speed.