The surge in online activities has led to the increasing popularity of sharing video data across diverse applications, including online education tutorials, social networking, video calling, and OTT platforms. Encryption prevents unauthorized access to the transmitted data over unreliable channels. The well-known features of chaos theory such as random behaviour, unpredictability, and initial parameters dependency facilitate its use in cryptography. Many security issues are faced by chaos-based cryptosystems because of their less complexity. Hence, a new Cosine-Cosine chaotic map characterized by intricate chaotic behaviour is designed in the current study. Additionally, we formulate an original video encryption scheme employing this Cosine-Cosine chaotic map. The encryption process involves five steps, beginning with the segmentation of the original video into frames based on its frame rate. In the second phase, a 384 bits pseudorandom key is generated that is further divided into three subkeys of 128 bits each. The novel Cosine-Cosine chaotic map-based sequence is generated. In the fourth step, red, green, and blue components are encrypted using the pseudorandom key and the chaotic sequence. In the last step, we combine encrypted frames to get cipher video. The security analysis validates that the proposed encryption protects against eavesdropping.