The IoT consists of a vast number of interconnected sensors, and ensuring secure communications between these sensors is a crucial concern. In this study, we apply chaos theory to the security of real-time communications in the IoT. Chaos theory has been increasingly utilized in cryptography in recent years, with the proposal of numerous stream ciphers based on chaos. We merge different 1D chaotic maps and construct a hybrid keystream generator. To increase the randomness and linear complexity of the output sequence, we use a nonlinear Dawson’s summation generator (DSG) to mix different chaotic outputs. The proposed keystream generator is suitable for real-time IoT communications as it features a low computational load and an improved throughput. Our analysis of the proposed keystream generator includes an evaluation of its resilience against known attacks, a measurement of its linear complexity, and statistical random number tests on the output keystream. The proposed keystream generator achieved a pass rate of 100% for the statistical test of the FIPS PUB 140-1 standard and a pass rate of at least 96% for that of the NIST SP800-22 standard.