A chapeau is a flat-topped hat once worn by senior clerics.
In European ecclesiastical heraldry, it is used as a mark of ecclesiastical dignity, especially that of cardinals, where it is called the red chapeau. It is worn over the shield by way of crest, as mitres and coronets are. A galero chapeau is flat, very narrow atop, but with a broad brim, adorned with long silken strings interlaced; suspended from within with rows of tassels, called by the Italians fiocchi, increasing in number as they come lower. The hat was given to them by Innocent IV in 1250, but was not used in arms till the year 1300. Until that time, the cardinals were represented with mitres. Archbishops and patriarchs bore a green hat, with four rows of tassels; bishops wore the same color, but with three; abbots and apostolical prothonotaries with two.
The chapeau is also sometimes used as a mark of secular dignity, such as a cap or coronet armed with ermine, worn by dukes, etc. The crest is borne on the chapeau, and by the chapeau the crest and armorial shield are separated, it being a rule that no crest should touch the shield immediately.
Some forms of bicorne were designed to be folded flat, so that they could be conveniently tucked underneath the arm when not being worn. A bicorne of this style is also known as a chapeau-bras or chapeau-de-bras (literally "arm-hat").
This article incorporates text from a publication now in the public domain: Chambers, Ephraim, ed. (1728). "Chapeau". Cyclopædia, or an Universal Dictionary of Arts and Sciences (1st ed.). James and John Knapton, et al.