Chain-of-Thought (CoT) enhances an LLM's ability to perform complex reasoning tasks, but it also introduces new security issues. In this work, we present ShadowCoT, a novel backdoor attack framework that targets the internal reasoning mechanism of LLMs. Unlike prior token-level or prompt-based attacks, ShadowCoT directly manipulates the model's cognitive reasoning path, enabling it to hijack multi-step reasoning chains and produce logically coherent but adversarial outcomes. By conditioning on internal reasoning states, ShadowCoT learns to recognize and selectively disrupt key reasoning steps, effectively mounting a self-reflective cognitive attack within the target model. Our approach introduces a lightweight yet effective multi-stage injection pipeline, which selectively rewires attention pathways and perturbs intermediate representations with minimal parameter overhead (only 0.15% updated). ShadowCoT further leverages reinforcement learning and reasoning chain pollution (RCP) to autonomously synthesize stealthy adversarial CoTs that remain undetectable to advanced defenses. Extensive experiments across diverse reasoning benchmarks and LLMs show that ShadowCoT consistently achieves high Attack Success Rate (94.4%) and Hijacking Success Rate (88.4%) while preserving benign performance. These results reveal an emergent class of cognition-level threats and highlight the urgent need for defenses beyond shallow surface-level consistency.