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Easily, with an interim acting chair. Upheaval under all contingencies is minimized with this solution.

Yes why is it any different to any other job - the deputy does the job,

Can you imagine a physics class taught by a grad student?

Half the job of the chair is to manage the human side of the department's priorities, including resolving disputes between faculty. You need moral authority, which a grad doesn't have.

The scale is about the same, and as someone else mentioned near here, the deputy chair would take over.