Zero-Knowledge Proofs (ZKPs) are rapidly gaining importance in privacy-preserving and verifiable computing. ZKPs enable a proving party to prove the truth of a statement to a verifying party without revealing anything else. ZKPs have applications in blockchain technologies, verifiable machine learning, and electronic voting, but have yet to see widespread adoption due to the computational complexity of the proving process. Recent works have accelerated the key primitives of state-of-the-art ZKP protocols on GPU and ASIC. However, the protocols accelerated thus far face one of two challenges: they either require a trusted setup for each application, or they generate larger proof sizes with higher verification costs, limiting their applicability in scenarios with numerous verifiers or strict verification time constraints. This work presents an accelerator, zkSpeed, for HyperPlonk, a state-of-the-art ZKP protocol that supports both one-time, universal setup and small proof sizes for typical ZKP applications in publicly verifiable, consensus-based systems. We accelerate the entire protocol, including two major primitives: SumCheck and Multi-scalar Multiplications (MSMs). We develop a full-chip architecture using 366.46 mm$^2$ and 2 TB/s of bandwidth to accelerate the entire proof generation process, achieving geometric mean speedups of 801$\times$ over CPU baselines.