Chip straw, used for bonnets, was not actually made of straw, but of thin pieces of wood. Chip could be plaited or woven just like straw but was sturdier, less flexible. Once formed into a sort of basket in whatever shape was currently fashionable, it could be bleached or colored, then trimmed with as desired.
Silk bonnets sometimes had chip and wire sewn into the seams, creating a framework to give them shape.
The image shown is a detail from "Promenade Dresses," Fashions of London and Paris, September 1804.