The task of predicting multiple links within knowledge graphs (KGs) stands as a challenge in the field of knowledge graph analysis, a challenge increasingly resolvable due to advancements in natural language processing (NLP) and KG embedding techniques. This paper introduces a novel methodology, the Knowledge Graph Large Language Model Framework (KG-LLM), which leverages pivotal NLP paradigms, including chain-of-thought (CoT) prompting and in-context learning (ICL), to enhance multi-hop link prediction in KGs. By converting the KG to a CoT prompt, our framework is designed to discern and learn the latent representations of entities and their interrelations. To show the efficacy of the KG-LLM Framework, we fine-tune three leading Large Language Models (LLMs) within this framework, employing both non-ICL and ICL tasks for a comprehensive evaluation. Further, we explore the framework's potential to provide LLMs with zero-shot capabilities for handling previously unseen prompts. Our experimental findings discover that integrating ICL and CoT not only augments the performance of our approach but also significantly boosts the models' generalization capacity, thereby ensuring more precise predictions in unfamiliar scenarios.