AI Planning is concerned with the selection of actions towards achieving a goal. Research on cellular automata (CA) is concerned with the question how global behaviours arise from local updating rules relating a cell to its direct neighbours. While these two areas are disparate at first glance, we herein identify a problem that is interesting to both: How to reach a fixed point in an asynchronous CA where cells are updated one-by-one? Considering a particular local updating rule, we encode this problem into PDDL and show that the resulting benchmark is an interesting challenge for AI Planning. For example, our experiments determine that, very atypically, an optimal SAT-based planner outperforms state-of-the-art satisficing heuristic search planners. This points to a severe weakness of current heuristics because, as we prove herein, plans for this problem can always be constructed in time linear in the size of the automaton. Our proof of this starts from a high-level argument and then relies on using a planner for flexible case enumeration within localised parts of the argument. Besides the formal result itself, this establishes a new proof technique for CAs and thus demonstrates that the potential benefit of research crossing the two fields is mutual.