Safety constraints are essential for reinforcement learning (RL) applied in real-world situations. Chance constraints are suitable to represent the safety requirements in stochastic systems. Most existing RL methods with chance constraints have a low convergence rate, and only learn a conservative policy. In this paper, we propose a model-based chance constrained actor-critic (CCAC) algorithm which can efficiently learn a safe and non-conservative policy. Different from existing methods that optimize a conservative lower bound, CCAC directly solves the original chance constrained problems, where the objective function and safe probability is simultaneously optimized with adaptive weights. In order to improve the convergence rate, CCAC utilizes the gradient of dynamic model to accelerate policy optimization. The effectiveness of CCAC is demonstrated by an aggressive car-following task. Experiments indicate that compared with previous methods, CCAC improves the performance by 57.6% while guaranteeing safety, with a five times faster convergence rate.