Consensus building is inherently challenging due to the diverse opinions held by stakeholders. Effective facilitation is crucial to support the consensus building process and enable efficient group decision making. However, the effectiveness of facilitation is often constrained by human factors such as limited experience and scalability. In this research, we propose a Parallel Thinking-based Facilitation Agent (PTFA) that facilitates online, text-based consensus building processes. The PTFA automatically collects real-time textual input and leverages large language models (LLMs) to perform all six distinct roles of the well-established Six Thinking Hats technique in parallel thinking. To illustrate the potential of the agent, a pilot study was conducted, demonstrating its capabilities in idea generation, emotional probing, and deeper analysis of idea quality. Additionally, future open research challenges such as optimizing scheduling and managing behaviors in divergent phase are identified. Furthermore, a comprehensive dataset that contains not only the conversational content among the participants but also between the participants and the agent is constructed for future study.