This paper presents a conjecture on the maximum rate of growth of chaos in thermal quantum systems with many degrees of freedom. The authors propose that the Lyapunov exponent, which measures the rate of exponential divergence of nearby trajectories in chaotic systems, is bounded by $ \lambda_L \leq \frac{2\pi k_B T}{\hbar} $, where $ T $ is the temperature of the system. This bound is derived using a combination of mathematical analysis and physical arguments, including the study of out-of-time-order correlation functions and the behavior of quantum systems in the semiclassical limit. The paper discusses various examples and motivations for this bound, including large N gauge theories, extended local systems, and systems with no bound on chaos. It also explores the implications of this bound in different physical contexts, such as Rindler space and semiclassical billiards. The authors argue that the bound is consistent with the behavior of chaotic systems in both quantum and classical regimes, and that it provides a general framework for understanding the growth of chaos in thermal quantum systems. The paper concludes with a discussion of the broader implications of this bound for the study of quantum systems and their dual gravitational descriptions.This paper presents a conjecture on the maximum rate of growth of chaos in thermal quantum systems with many degrees of freedom. The authors propose that the Lyapunov exponent, which measures the rate of exponential divergence of nearby trajectories in chaotic systems, is bounded by $ \lambda_L \leq \frac{2\pi k_B T}{\hbar} $, where $ T $ is the temperature of the system. This bound is derived using a combination of mathematical analysis and physical arguments, including the study of out-of-time-order correlation functions and the behavior of quantum systems in the semiclassical limit. The paper discusses various examples and motivations for this bound, including large N gauge theories, extended local systems, and systems with no bound on chaos. It also explores the implications of this bound in different physical contexts, such as Rindler space and semiclassical billiards. The authors argue that the bound is consistent with the behavior of chaotic systems in both quantum and classical regimes, and that it provides a general framework for understanding the growth of chaos in thermal quantum systems. The paper concludes with a discussion of the broader implications of this bound for the study of quantum systems and their dual gravitational descriptions.