hatband

from WordNet (r) 3.0 (2006)

hatband
    n 1: a band around the crown of a hat just above the brim

from The Collaborative International Dictionary of English v.0.48

Hatband \Hat"band`\ (h[a^]t"b[a^]nd`), n.
   A band round the crown of a hat; sometimes, a band of black
   cloth, crape, etc., worn as a badge of mourning.
   [1913 Webster]