Chaotic systems are used in various applications due to their high security and complexity. Because minor changes in parameters have a significant effect on the output values and the dynamic behavior of the system. Besides, security and robustness are the most important requirements of data hiding. Therefore, in this paper, it is proposed to use chaos-based data hiding for videos. The merits of the proposed method are selection of embedding location with robust system, increasing the secret data capacity, and keep the visual quality, which are in trade-off for existing methods. Because, in the existing methods the secret message is embedded into pixels of a consecutive, a selected or a random frame. Another deficiency of existing methods is embedding capacity. They embed fewer secret data to keep the visual quality of the stego object. However, compared to the drawback of existing literature, in the proposed method the secret message is embedded in entire video with 4D chaotic system, which is also an important novelty of this paper.The proposed method evaluated by objective criteria and achieved valuable results. The histogram analysis proves our method is undetectable. For different high ratios of embedding capacity, the visual quality of the stego videos is high where the average PSNR is about 55 dB, and MS-SSIM is closed to 1. The proposed method's results compared chaotic and non-chaotic video steganography methods. Our methods achieve 54.92 dB for embedding ratio 8.08% where the results are 53.57 dB and 5% for the best existing non-chaotic method and 49.99 dB and 0.001% for the best chaotic method, for similar capacity the proposed method gives superior visual performance over the chaotic literature. Finally, the robustness analysis with pixel value attack and lsb attack shows the proposed method appears to be resistant to these types of attacks.