Molecule generation requires satisfying multiple chemical and biological constraints while searching a large and structured chemical space. This makes it a non-binary problem, where effective models must identify non-obvious solutions under constraints while maintaining exploration to improve success by escaping local optima. From this perspective, creativity is a functional requirement in molecular generation rather than an aesthetic notion. Large language models (LLMs) can generate molecular representations directly from natural language prompts, but it remains unclear what type of creativity they exhibit in this setting and how it should be evaluated. In this work, we study the creative behavior of LLMs in molecular generation through a systematic empirical evaluation across physicochemical, ADMET, and biological activity tasks. We characterize creativity along two complementary dimensions, convergent creativity and divergent creativity, and analyze how different factors shape these behaviors. Our results indicate that LLMs exhibit distinct patterns of creative behavior in molecule generation, such as an increase in constraint satisfaction when additional constraints are imposed. Overall, our work is the first to reframe the abilities required for molecule generation as creativity, providing a systematic understanding of creativity in LLM-based molecular generation and clarifying the appropriate use of LLMs in molecular discovery pipelines.