Hypergraphs are marked by complex topology, expressing higher-order interactions among multiple nodes with hyperedges, and better capturing the topology is essential for effective representation learning. Recent advances in generative self-supervised learning (SSL) suggest that hypergraph neural networks (HNNs) learned from generative self-supervision have the potential to effectively encode the complex hypergraph topology. Designing a generative SSL strategy for hypergraphs, however, is not straightforward. Questions remain with regard to its generative SSL task, connection to downstream tasks, and empirical properties of learned representations. In light of the promises and challenges, we propose a novel generative SSL strategy for hypergraphs. We first present a generative SSL task on hypergraphs, hyperedge filling, and highlight its theoretical connection to node classification. Based on the generative SSL task, we propose a hypergraph SSL method, HYPEBOY. HYPEBOY learns effective general-purpose hypergraph representations, outperforming 15 baseline methods across 11 benchmark datasets. To our knowledge, this is the first study on generative SSL on hypergraphs, and we demonstrate its theoretical and empirical strengths for hypergraph representation learning.