The field of AI alignment aims to steer AI systems toward human goals, preferences, and ethical principles. Its contributions have been instrumental for improving the output quality, safety, and trustworthiness of today's AI models. This perspective article draws attention to a fundamental challenge we see in all AI alignment endeavors, which we term the "AI alignment paradox": The better we align AI models with our values, the easier we may make it for adversaries to misalign the models. We illustrate the paradox by sketching three concrete example incarnations for the case of language models, each corresponding to a distinct way in which adversaries might exploit the paradox. With AI's increasing real-world impact, it is imperative that a broad community of researchers be aware of the AI alignment paradox and work to find ways to mitigate it, in order to ensure the beneficial use of AI for the good of humanity.