Blockchain consensus mechanisms have relied on algorithms such as Proof-of-Work (PoW) and Proof-of-Stake (PoS) to ensure network functionality and integrity. However, these approaches struggle with adaptability for decision-making where the opinions of each matter rather than reaching an agreement based on honest majority or weighted consensus. This paper introduces a novel deliberation-based consensus mechanism where Large Language Models (LLMs) act as rational agents engaging in structured discussions to reach a unanimous consensus. By leveraging graded consensus and a multi-round deliberation process, our approach ensures unanimous consensus for definitive problems and graded consensus for prioritized decision problems and policies. We provide a formalization of our system and use it to show that the properties of blockchains are maintained, while also addressing the behavior in terms of adversaries, stalled deliberations, and confidence in consensus. Moreover, experimental results demonstrate system feasibility, showcasing convergence, block properties, and accuracy, which enable deliberative decision-making on blockchain networks.