The 11th Doctor frequently (but not always) wore a fob chain with his waistcoats.
He wore the chain in the mysterious publicity photos for “The Bells of Saint John” (although again, he didn’t wear the waistcoat in that episode).
He wore the fob chain with his waistcoat during “The Rings of Akhaten.”
However, he only wore the fob chain in some of the publicity photos for that episode.
In this particular publicity photo (and a second, onto which he was presumably photoshopped), he didn’t.
He didn’t wear the fob chain in the following episode, “Cold War.”
Neither did he wear the chain the publicity photos for the episode.
He also didn’t wear the fob chain in the next episode, “Hide.”
As with “Cold War,” he didn’t wear the fob chain for the “Hide” publicity photos, either.
He did wear the fob chain throughout the entirety of the next episode, “Journey to the Center of the TARDIS.”
He also wore the fob chain with his “scales” waistcoat during its final, brief appearance near the beginning of “The Time of the Doctor.”
Here are some detail shots of the fob chain.
In these particular images, the clasp on the underside was actually visible.