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With incredible speed Large Language Models (LLMs) are reshaping many aspects of society. This has been met with unease by the public, and public discourse is rife with questions about whether LLMs are or might be conscious. Because there is widespread disagreement about consciousness among scientists, any concrete answers that could be offered the public would be contentious. This paper offers the next best thing: charting the possibility of consciousness in LLMs. So, while it is too early to judge concerning the possibility of LLM consciousness, our charting of the possibility space for this may serve as a temporary guide for theorizing about it.