We introduce ChemPro, a progressive benchmark with 4100 natural language question-answer pairs in Chemistry, across 4 coherent sections of difficulty designed to assess the proficiency of Large Language Models (LLMs) in a broad spectrum of general chemistry topics. We include Multiple Choice Questions and Numerical Questions spread across fine-grained information recall, long-horizon reasoning, multi-concept questions, problem-solving with nuanced articulation, and straightforward questions in a balanced ratio, effectively covering Bio-Chemistry, Inorganic-Chemistry, Organic-Chemistry and Physical-Chemistry. ChemPro is carefully designed analogous to a student's academic evaluation for basic to high-school chemistry. A gradual increase in the question difficulty rigorously tests the ability of LLMs to progress from solving basic problems to solving more sophisticated challenges. We evaluate 45+7 state-of-the-art LLMs, spanning both open-source and proprietary variants, and our analysis reveals that while LLMs perform well on basic chemistry questions, their accuracy declines with different types and levels of complexity. These findings highlight the critical limitations of LLMs in general scientific reasoning and understanding and point towards understudied dimensions of difficulty, emphasizing the need for more robust methodologies to improve LLMs.