A polished agate cup, mounted on a medieval gold-and-jasper base, kept in the small Chapel of the Holy Chalice off the cathedral's south transept. Catholic tradition — and a serious thread of academic argument — identifies the agate cup as the actual chalice used at the Last Supper, brought to Spain in the early Christian centuries via Rome and the monasteries of Aragon, where it has lived since 1437.
Whether or not you believe it, the object is genuinely from the right time and place (first-century BC, Antioch or Alexandria) and is the most plausible Grail candidate in existence. The chapel itself is a beautifully proportioned 14th-century space, often quietly busy with pilgrims.