Traditional ontologies excel at describing domain structure but cannot generate novel artifacts. Large language models generate fluently but produce outputs that lack structural validity, hallucinating mechanisms without components, goals without end conditions. We introduce Generative Ontology, a framework that synthesizes these complementary strengths: ontology provides the grammar; the LLM provides the creativity. Generative Ontology encodes domain knowledge as executable Pydantic schemas that constrain LLM generation via DSPy signatures. A multi-agent pipeline assigns specialized roles to different ontology domains: a Mechanics Architect designs game systems, a Theme Weaver integrates narrative, a Balance Critic identifies exploits. Each agent carrying a professional "anxiety" that prevents shallow, agreeable outputs. Retrieval-augmented generation grounds novel designs in precedents from existing exemplars, while iterative validation ensures coherence between mechanisms and components. We demonstrate the framework through GameGrammar, a system for generating complete tabletop game designs. Given a thematic prompt ("bioluminescent fungi competing in a cave ecosystem"), the pipeline produces structurally complete, playable game specifications with mechanisms, components, victory conditions, and setup instructions. These outputs satisfy ontological constraints while remaining genuinely creative. The pattern generalizes beyond games. Any domain with expert vocabulary, validity constraints, and accumulated exemplars (music composition, software architecture, culinary arts) is a candidate for Generative Ontology. We argue that constraints do not limit creativity but enable it: just as grammar makes poetry possible, ontology makes structured generation possible.