Large Language Models (LLMs) are making waves in software development, but can they truly optimize code at a low level? Researchers have explored this question by focusing on a fundamental compiler optimization technique called peephole optimization. This technique makes small, localized changes within short sequences of assembly code, offering a perfect testing ground for LLMs' abilities. The study used the 7B-parameter Llama2 model as a baseline, fine-tuning it on a large dataset of AArch64 assembly code. While Llama2 achieved decent scores on metrics like BLEU, a deeper dive revealed a critical flaw: it consistently generated nonsensical instructions, highlighting the limitations of current LLMs in truly understanding code structure. Interestingly, the fine-tuning process itself seemed to hinder Llama2's ability to generalize to code it hadn't seen before. When compared to OpenAI's GPT-4o and the newer GPT-o1, a surprising trend emerged. GPT-o1, empowered by its chain-of-thought reasoning, significantly outperformed both Llama2 and GPT-4o, even generating *better* code than the original compiler in some cases. This superior performance came at the cost of increased processing time and inference steps, suggesting that true code optimization with LLMs might require a different approach than simple fine-tuning. The chain-of-thought process in GPT-o1 allowed it to break down the optimization problem step-by-step, mimicking human reasoning. This suggests a bright future for LLM-based optimization, where models not only generate code but understand its underlying logic, paving the way for compilers that can adapt and optimize code in ways we can only imagine today.