Chakin (茶巾) is a linen cloth used in Temae.
In most temae it is used to wipe Chawan before and between each bowl of tea. It is also used with Mizutsugi and Yakkan to prevent drops at the sprout. In Gozumi it is used to lift on and of the Kama lid and wipe/purify the kama it self.
Most of the time it is already folded when it is brought in to the room, but in some temae it is folded or refolded in the room: