What about the inverse, is there any state where a Republican could win while winning just one county, or where this might be possible one day?
Despite the example of Hawaii given for this, it's probably the most likely state for the inverse.
Might be possible in Rhode Island if you somehow had a Republican who won Kent County by a huge margin and lost everywhere else narrowly, but it's kind of hard to imagine what sort of matchup would result in a Democrat winning the rural counties and only narrowly winning Providence.