A closure device for a container has a lid element for closing the container opening, a chamber which is arranged on the lid element for storing a medium, and an inner housing. The chamber and the inner housing have corresponding closure means and opening means. A discharge opening paired with the chamber can be released by moving the lid element relative to the inner housing such that a medium can exit the chamber into the container. The chamber and the inner housing each have a corresponding first thread which is formed relative to a winding rotational axis. The first thread which is located on the chamber is arranged so as to point radially outwards when seen from the thread rotational axis.