How should one design unprecedented democratic processes capable of handling enormous sets of alternatives like all possible policies, bills, or statements? I argue that this challenge can be addressed through a framework called generative social choice, which fuses the rigor of social choice theory with the flexibility and power of large language models. I then explore an application of generative social choice to the problem of identifying a proportionally representative slate of opinion statements. This includes a discussion of desired properties, an algorithm that provably achieves them, an implementation using GPT, and insights from an end-to-end pilot. By providing guarantees, generative social choice could alleviate concerns about AI-driven democratic innovation and help unlock its potential.