Eleven years after the ascension of Our Blessed Lord, St. Peter who had been appointed the head of the Church on earth by Christ Himself, transferred the seat of the Papacy from Antioch to Rome, where he preached the Faith and established his episcopal chair, and there the Bishops of Rome have been ever since accounted his successors.  The feast of the Chair of St. Peter is that of the foundation of the See of Rome.  From the Third Century it was symbolized by a chair carved in wood or tufa, a relic now kept high in the apse of the Vatican Basilica.

Taken from: Butler’s Lives of the Saints