In an era where global connectivity has become critical, satellite communication is essential for businesses, governments, and individuals. Widely used services with satellite communication such as climate change monitoring, military surveillance and real-time event broadcasting, involve data in the form of images rather text. Therefore, securing image transmission in satellite communication using efficient and effective encryption approaches, has gained a significant attention from academia as well as the industry. In this paper, we specifically focus on chaos based image encryption as one of the key privacy-preserving techniques for satellite communication. While there are several privacy enhancing techniques for protecting image data but chaos based encryption has distinct advantages such as high flexibility, high security, less computational overheads, less computing power and ease of implementation. First, we present a solid background about satellite communication and image encryption in satellite communication, covering theoretical aspects of chaotic systems and their practical usage for image encryption. Next we present a comprehensive literature review on all state-of-the-art studies specifically for chaos based satellite image encryption, with a detailed analysis of the evaluation process, including evaluation parameters and conditions. Finally, we discuss about existing challenges and open research problems for chaos based satellite image encryption.