This paper introduces a novel approach to addressing the security challenges of the Internet of Things (IoT) by presenting a secure Chaos-based lightweight cryptosystem. The proposed design incorporates a Pseudo-Chaotic Numbers Generator combined with the Speck64/128 lightweight block cipher, to meet the stringent requirements of security and lightweight characteristics. First, we subject the cryptosystem to a battery of rigorous tests, including various cryptanalytics such as brute-force, differential attacks, and statistical attacks. The results of these tests clearly demonstrate the cryptosystem's exceptional security resilience and its capacity to effectively withstand these attacks. Then, the novel cryptosystem architecture, specifically designed for resource-limited applications like IoT, was implemented on a Xilinx PYNQ-Z2 XC7Z020 FPGA platform, which aligns perfectly with the constraints of IoT devices. The investigation comprises a thorough analysis and evaluation of the developed cryptosystem according to the algorithm complexity and the achieved precision, hardware area, maximum operational frequency, throughput, efficiency, and power consumption. The findings prove the effectiveness of our approach in terms of computational complexity, memory requirements, and power consumption. Eventually, after reviewing and comparing our results to the existing literature, our cryptosystem's superiority becomes evident. The simulation results and performance analysis show that the proposed Chaos-Based Lightweight Cryptosystem (SCBLC) can be considered an ideal choice for securing communication in IoT devices with limited resources, making significant strides toward enhancing IoT network security.