The font "Couture" by Chase Babb is definitely not this font, "Couture" is a reproduction. As mentioned, what we understand as the original font must be logotype. It appears to have been developed from the styling of the linked Cs of the logo. The logo was not "designed" by Gabrielle Chanel, although it may have been "styled" by her to give it the characteristic hard lines and corners we recognise. It was "inspired" for her by existing decorations at the Château de Crémat, it was the "logo" of that place and was created (by a person unknown to me at time of writing this) when the castle was built in 1906 by vintner Antoine Marie. As already mentioned it has also been developed by Chanel (corporation) to be a font. You can see the font when the credits roll for Lagerfeld's film "The Return". I don't know the name of the font but I bet it's called something like "The font that is the exclusive property of Chanel Corporation".