The paper proposes a secure and robust stereo image watermarking scheme based on chaotic logistic map encoding and frequency transformations. The chaotic logistic map encoding is employed to confuse both original stereo images and watermarked images. Since the high sensitivity to initial conditions introduced in the chaotic logistic map, a huge key space is provided for encoding images. Thus, the proposed system has a strong secure capability to resist brute-force and statistical attacks, in which the evaluation goes through various analysis methods such as sensitive key analysis, correlative adjacent pixels analysis. Moreover, to enhance the robustness of the watermarked image, the discrete cosine transform (DCT) and the singular value decomposition (SVD) are exploited for this purpose. Based upon the properties of the SVD and utilizing the advantages of the DCT, a watermarked image is embedded in the singular value. Performance evaluations show that the proposed watermarking scheme for stereo images is highly secure as well as strongly robust against different kinds of attacks.