Text generation under constraints have seen increasing interests in natural language processing, especially with the rapidly improving capabilities of large language models. However, existing benchmarks for constrained generation usually focus on fixed constraint types (e.g. generate a sentence containing certain words) that have proved to be easy for state-of-the-art models like GPT-4. We present COLLIE, a grammar-based framework that allows the specification of rich, compositional constraints with diverse generation levels (word, sentence, paragraph, passage) and modeling challenges (e.g. language understanding, logical reasoning, counting, semantic planning). We also develop tools for automatic extraction of task instances given a constraint structure and a raw text corpus. Using COLLIE, we compile the COLLIE-v1 dataset with 1,132 instances comprising 13 constraint structures. We perform systematic experiments across five state-of-the-art instruction-tuned language models and analyze their performances to reveal shortcomings. COLLIE is designed to be extensible and lightweight, and we hope the community finds it useful to develop more complex constraints and evaluations in the future.