While machine learning algorithms have been shown to excel at specific chemical tasks, they have struggled to capture the strategic thinking that characterizes expert chemical reasoning, limiting their widespread adoption. Here we demonstrate that large language models (LLMs) can serve as powerful chemical reasoning engines when integrated with traditional search algorithms, enabling a new approach to computer-aided chemistry that mirrors human expert thinking. Rather than using LLMs to directly manipulate chemical structures, we leverage their ability to evaluate chemical strategies and guide search algorithms toward chemically meaningful solutions. We demonstrate this paradigm through two fundamental challenges: strategy-aware retrosynthetic planning and mechanism elucidation. In retrosynthetic planning, our method allows chemists to specify desired synthetic strategies in natural language to find routes that satisfy these constraints in vast searches. In mechanism elucidation, LLMs guide the search for plausible reaction mechanisms by combining chemical principles with systematic exploration. Our approach shows strong performance across diverse chemical tasks, with larger models demonstrating increasingly sophisticated chemical reasoning. Our approach establishes a new paradigm for computer-aided chemistry that combines the strategic understanding of LLMs with the precision of traditional chemical tools, opening possibilities for more intuitive and powerful chemical reasoning systems.