By integrating Chain-of-Thought (CoT) reasoning, Vision-Language-Action (VLA) models have demonstrated strong capabilities in robotic manipulation, particularly by improving generalization and interpretability. However, the security of CoT-based reasoning mechanisms remains largely unexplored. In this paper, we show that CoT reasoning introduces a novel attack vector for targeted behavior hijacking--for example, causing a robot to mistakenly deliver a knife to a person instead of an apple--without modifying the user's instruction. We first provide empirical evidence that CoT strongly governs action generation, even when it is semantically misaligned with the input instructions. Building on this observation, we propose TRAP, the first targeted behavior-hijacking adversarial attack against CoT-reasoning VLA models. By targeting the reasoning-to-action pathway, TRAP uses an adversarial patch (e.g., a tablecloth placed on the table) to steer intermediate CoT reasoning and downstream actions toward adversary-defined behaviors. Extensive evaluations on three representative reasoning VLAs, spanning distinct CoT reasoning mechanisms, demonstrate the effectiveness of TRAP. Notably, we implemented the patch by printing it on paper in a real-world setting. Our findings highlight the urgent need to secure CoT reasoning in VLA systems. The project page is available at https://zhengxian-huang.github.io/TRAP-website/.