The Collaborative International Dictionary of English v.0.48:

Hairbreadth \Hair"breadth`\ (-br[e^]dth), Hair's breadth
\Hair's" breadth`\ (h[^a]rz"-).
   The diameter or breadth of a hair; a very small distance;
   sometimes, definitely, the forty-eighth part of an inch.
   [Also spelled hairsbreadth.]
   [1913 Webster]

         Every one could sling stones at an hairbreadth and not
         miss.                                    --Judg. xx.
                                                  16.
   [1913 Webster]