Large Language Models (LLMs) have demonstrated remarkable capabilities in performing tasks across various domains without needing explicit retraining. This capability, known as In-Context Learning (ICL), while impressive, exposes LLMs to a variety of adversarial prompts and jailbreaks that manipulate safety-trained LLMs into generating undesired or harmful output. In this paper, we propose a novel interpretation of ICL in LLMs through the lens of cognitive neuroscience, by drawing parallels between learning in human cognition with ICL. We applied the principles of Cognitive Load Theory in LLMs and empirically validate that similar to human cognition, LLMs also suffer from cognitive overload a state where the demand on cognitive processing exceeds the available capacity of the model, leading to potential errors. Furthermore, we demonstrated how an attacker can exploit ICL to jailbreak LLMs through deliberately designed prompts that induce cognitive overload on LLMs, thereby compromising the safety mechanisms of LLMs. We empirically validate this threat model by crafting various cognitive overload prompts and show that advanced models such as GPT-4, Claude-3.5 Sonnet, Claude-3 OPUS, Llama-3-70B-Instruct, Gemini-1.0-Pro, and Gemini-1.5-Pro can be successfully jailbroken, with attack success rates of up to 99.99%. Our findings highlight critical vulnerabilities in LLMs and underscore the urgency of developing robust safeguards. We propose integrating insights from cognitive load theory into the design and evaluation of LLMs to better anticipate and mitigate the risks of adversarial attacks. By expanding our experiments to encompass a broader range of models and by highlighting vulnerabilities in LLMs' ICL, we aim to ensure the development of safer and more reliable AI systems.