Anyone walking to the fortress, the funicular or to St. Peter's Cemetery will cross Kapitelplatz (Chapter Square). The spacious square is bordered on the south by the Cathedral, by the Cathedral provostry and archiepiscopal palace in the east, the novice's wing of St. Peter's Monastery in the west and the Cathedral Chapter's mills.
Chapter Square was once the site of the Cathedral Abbey: the high clergy resided on Chapter Square and in the palaces in the adjacent streets until the archbishopric was dissolved in 1803. The Cathedral district was comprised of austere, sovereign residences lined up on Kapitelgasse, Kaigasse and Chiemseegasse.

Slightly secluded from the spacious square, Chapter Fountain bears witness to the past: a horse pond was already situated in the center of Chapter Square during the Middle Ages. The new fountain was built under Archbishop Leopold Firmian in 1732 to plans by Franz Anton Danreiter, obviously modeled on Roman fountains. The ramp used by the horses to access the water leads straight up to the group of figures: Neptune, god of the sea, holding a trident and crown, mounted on a seahorse spurting water. The baroque figure was sculpted by Josef Anton Pfaffinger. A chronogram with Archbishop Firmian's coat of arms can be found above the niche.