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Despite the recent progress in deep learning-based face image colorization techniques, there is still much room for improvement. One of the significant challenges is the bias toward specific skin color. Moreover, the conventional face colorization approaches aim to produce colored 2D face images, whereas the generation of colored 3D faces from monocular achromatic (gray-scale) images is beyond the scope of these methods despite having immense potential applications. To address these issues, we propose Self-Supervised COoperative COlorizaTion of Achromatic Faces (COCOTA) framework that contains chromatic and achromatic pipelines to jointly estimate the color and shape of 3D faces using monocular achromatic face images without inducing any specific color bias. On the challenging CelebA test dataset, COCOTA out-performs the current state-of-the-art method by a large margin (e.g., for 3D color-based error, a reduction from 5.12 ± 0.13 to 3.09 ± 0.08 leading to an improvement of 39.6%), demonstrating the effectiveness of the proposed method.