The Chair of Peter’s first occupant was St. Peter and the most recent occupant is pope Benedict XVI. It’s not a real chair, but rather a seat (think parliamentary seat or judicial seat) or office in which the Father of the Church has traditionally sat.

St. Jerome wrote in 396 A.D.: "I follow no leader but Christ and join in communion with none but your blessedness [Pope Damasus I], that is, with the chair of Peter. I know that this is the rock on which the Church has been built. Whoever eats the Lamb outside this house is profane. Anyone who is not in the ark of Noah will perish when the flood prevails"

POPE (Catholic Encyclopedia)