Steganography is a technique to hide a secret message within a different multimedia carrier so that the secret message cannot be identified. The goals of steganography techniques include improvements in imperceptibility, information hiding, capacity, security, and robustness. In spite of numerous secure methodologies that have been introduced, there are ongoing attempts to develop these techniques to make them more secure and robust. This paper introduces a color image steganographic method based on a secret map, namely 3-D cat. The proposed method aims to embed data using a secure structure of chaotic steganography, ensuring better security. Rather than using the complete image for data hiding, the selection of the image band and pixel coordination is adopted, using the 3D map that produces irregular outputs for embedding a secret message randomly in the least significant bit (LSB) of the cover image. This increases the complexity encountered by the attackers. The performance of the proposed method was evaluated and the results reveal that the proposed method provides a high level of security through defeating various attacks, such as statistical attacks, with no detectable distortion in the stego-image. Comparison results ensure that the proposed method surpasses other existing steganographic methods regarding the Mean Square Error (MSE) and Peak Signal-to-Noise Ratio(PSNR).