The definition generation task aims to generate a word's definition within a specific context automatically. However, owing to the lack of datasets for different complexities, the definitions produced by models tend to keep the same complexity level. This paper proposes a novel task of generating definitions for a word with controllable complexity levels. Correspondingly, we introduce COMPILING, a dataset given detailed information about Chinese definitions, and each definition is labeled with its complexity levels. The COMPILING dataset includes 74,303 words and 106,882 definitions. To the best of our knowledge, it is the largest dataset of the Chinese definition generation task. We select various representative generation methods as baselines for this task and conduct evaluations, which illustrates that our dataset plays an outstanding role in assisting models in generating different complexity-level definitions. We believe that the COM-PILING dataset will benefit further research in complexity controllable definition generation.