The Vatican have so far only returned one piece of the Parthenon Marbles  from their collection – this article however hints that another of the two remaining ones will be on its way to Greece in the coming months.
Athens News Agency 
Vatican returns Parthenon fragment
A fragment of a Parthenon frieze returned to Greece by the Vatican’s Museum Gregoriano Etrusco was presented by Culture Minister Michalis Liapis stressing that “this gesture by one of the most important museums in Europe sets an example for others to follow and eventually restore the unity of the Parthenon Marbles”.
The special event on Wednesday was held at the New Museum of the Acropolis in the presence of Vatican’s ambassador to Greece Patrick Coveney, Greece’s ambassador to the Vatican M. Hiskakis, head of the Vatican museum’s classical antiquities department Giandomenico Spinola and Organization for the Construction of the New Museum of the Acropolis President Prof. Dimitris Pantermalis.
The fragment, returned on a one-year loan, is from a section of the Parthenon frieze depicting part of a youth’s head and part of a tray he carries.
The efforts for the return of the fragment were launched in the early 90s and intensified after 1997. The late Archbishop Christodoulos of Athens and All Greece had, during his visit to the Vatican in 2006, requested from Pope Benedict XVI that the fragment be returned.
Two more fragments are still kept at the Vatican museum, one of which will be returned to Athens soon.