This is a vintage high quality milan straw summer fedora hat.  It was made by the Champ Hat company in the late 1950s.  It has a nice brown leather sweatband, flat top porkpie styling, with a super wide band and back bow.  
Size: 7-1/4Brim Width: 2-1/8″Band Width: 2-1/2″Crown Height:  4″