The First Vatican Council decrees the dogma of papal infallibility.

The First Ecumenical Council of the Vatican, commonly known as the First Vatican Council or Vatican I, was the 20th ecumenical council of the Catholic Church, held three centuries after the preceding Council of Trent which was adjourned in 1563. The council was convoked by Pope Pius IX on 29 June 1868, under the rising threat of the Kingdom of Italy encroaching on the Papal States. It opened on 8 December 1869 and was adjourned on 20 September 1870 after the Italian Capture of Rome. Its best-known decision is its definition of papal infallibility.

Papal infallibility is a dogma of the Catholic Church which states that, in virtue of the promise of Jesus to Peter, the Pope when he speaks ex cathedra is preserved from the possibility of error on doctrine "initially given to the apostolic Church and handed down in Scripture and tradition". It does not mean that the pope cannot sin or otherwise err in many cases, though he is prevented by the assistance of the Holy Spirit from issuing heretical teaching even in his non-infallible Magisterium, as a corollary of indefectibility. This doctrine, defined dogmatically at the First Vatican Council of 1869–1870 in the document Pastor aeternus, is claimed to have existed in medieval theology and to have been the majority opinion at the time of the Counter-Reformation.