AI-based colorization has shown remarkable capability in generating realistic color images from grayscale inputs. However, it poses risks of copyright infringement -- for example, the unauthorized colorization and resale of monochrome manga and films. Despite these concerns, no effective method currently exists to prevent such misuse. To address this, we introduce the first defensive paradigm, Uncolorable Examples, which embed imperceptible perturbations into grayscale images to invalidate unauthorized colorization. To ensure real-world applicability, we establish four criteria: effectiveness, imperceptibility, transferability, and robustness. Our method, Perception-Aware Chroma-Restrictive Perturbation (PAChroma), generates Uncolorable Examples that meet these four criteria by optimizing imperceptible perturbations with a Laplacian filter to preserve perceptual quality, and applying diverse input transformations during optimization to enhance transferability across models and robustness against common post-processing (e.g., compression). Experiments on ImageNet and Danbooru datasets demonstrate that PAChroma effectively degrades colorization quality while maintaining the visual appearance. This work marks the first step toward protecting visual content from illegitimate AI colorization, paving the way for copyright-aware defenses in generative media.