Many critical scientific and societal challenges involve interactions among groups of entities that cannot be adequately represented as simple pairwise relationships. For example, chemical reactions, biological signaling pathways, social group dynamics, and epidemic spread involve simultaneous multi-way interactions among more than two entities. Hypergraphs, a mathematical generalization of traditional graphs, provide a more accurate representation by allowing a single edge to connect any number of entities. Despite rapidly growing adoption of hypergraph-based models across biology, health sciences, social networks, and artificial intelligence, researchers lack the scalable, comprehensive, and user-friendly software needed to analyze hypergraphs effectively. This gap forces scientists to rely on simplified graph models that risk losing critical higher-order relationships in their data, potentially leading to incomplete scientific conclusions. This motivates the project - CHAI (Cyberinfrastructure for Hypergraph-based Analysis and Innovation), an open-source parallel software framework that addresses this critical gap. CHAI serves a broad scientific user base through a tiered interface accommodating users ranging from domain scientists who need ready-to-use analytical functions, to intermediate users who wish to tune algorithms, to advanced developers creating entirely new methods. For real-world validation, the CHAI team collaborates with researchers from social network analysis, bioinformatics, food web ecology, additive manufacturing, unmanned aerial vehicles, and cyber-physical systems. The CHAI project aims to develop three foundational technical innovations: (i) a unified data structure that efficiently supports both static and dynamic hypergraph representations on high performance computing platforms including GPUs, (ii) a compact motif-based representation that reduces memory requirements and accelerates hypergraph analysis, and (iii) an extensible paralle