Jeannette catalogs called this blue "delfite". The advertising on the underside of the hat is a very unusual find; the underside is usually blank and unmarked. I've only seen 3 of these. Presumably, the hats with advertising were used by the company at shows for sales representatives.
The hats (and the color) were introduced in 1936 and sold as souvenirs at the Texas Centennial celebration. (Comment from Suzanne.)