Is there one?
I can't find any. The closest I could find was Macon county Alabama, which very narrowly went for Eisenhower in 1956.
Just went through the county maps and there isn't any. Goldwater 1964, Wallace 1968, and Nixon 1972 really ruined the chances of this happening. Several states were complete Republican sweeps. There's a fair number of Thurmond counties which are safe D today, although it is worth noting that the folks who vote Democrat in the South these days were mostly disenfranchised pre 1965.