<p>This paper introduces a new three-dimensional hybrid Lorenz–Chua chaotic system that integrates a piecewise linear absolute-value nonlinearity within the z-equation. The system combines the bilinear coupling structure of the Lorenz oscillator with the switching characteristics of the Chua family, forming a hybrid topology capable of generating rich chaotic dynamics such as a period doubling route to chaos and coexisting attractors. Numerical analyses based on Lyapunov exponents, bifurcation diagrams, phase portraits and Poincaré sections confirm the presence of complex attractors and strong sensitivity to initial conditions. Leveraging these properties, the proposed chaotic model is embedded into a third-order discrete-time delta–sigma modulator to enhance security and noise resilience in biomedical data transmission. The chaotic delta–sigma modulator achieves simultaneous signal quantization and encryption, enabling secure, power-efficient telemedicine of electrocardiogram (ECG) and electroencephalogram (EEG) signals over open communication channels. Simulation results demonstrate high-quality signal reconstruction, strong resistance to external interference, and dynamic key variability. The proposed system thus bridges nonlinear dynamics and biomedical signal processing, offering a promising framework for secure and efficient telehealth communication systems.</p>