Large language models (LLMs) have recently demonstrated state-of-the-art performance across various natural language processing (NLP) tasks, achieving near-human levels in multiple language understanding challenges and aligning closely with the core principles of semantic communication. Inspired by LLMs' advancements in semantic processing, we propose an innovative LLM-enabled semantic communication system framework, named LLM-SC, that applies LLMs directly to the physical layer coding and decoding for the first time. By analyzing the relationship between the training process of LLMs and the optimization objectives of semantic communication, we propose training a semantic encoder through LLMs' tokenizer training and establishing a semantic knowledge base via the LLMs' unsupervised pre-training process. This knowledge base aids in constructing the optimal decoder by providing the prior probability of the transmitted language sequence. Based on this foundation, we derive the optimal decoding criterion for the receiver and introduce the beam search algorithm to further reduce the complexity. Furthermore, we assert that existing LLMs can be employed directly for LLM-SC without additional re-training or fine-tuning. Simulation results demonstrate that LLM-SC outperforms classical DeepSC at signal-to-noise ratios (SNR) exceeding 3 dB, enabling error-free transmission of semantic information under high SNR, which is unattainable by DeepSC. In addition to semantic-level performance, LLM-SC demonstrates compatibility with technical-level performance, achieving approximately 8 dB coding gain for a bit error ratio (BER) of $10^{-3}$ without any channel coding while maintaining the same joint source-channel coding rate as traditional communication systems.