From: 'St. Peter's - Guide to the Basilica and Square'
The Clementine Chapel was commissioned by Pope Clement VIII (1592-1605), whose coat of arms stands out against the paving. It was begun by Michelangelo and completed by Giacomo Della Porta (1540-1602) for the Jubilee in 1600. The altar is dedicated to St. Gregory the Great (590-604). In a sarcophagus beneath the altar his remains are preserved, brought here in 1606. This Pope, also called the "Savior of the Church" and the "Defender of Rome", is associated with the name of the Gregorian chant or plainsong which he promoted.

From: 'The Basilica of Saint Peter in the Vatican' by Franco Cosimo Panini
Conceived as a pendant to the Gregorian Chapel on the other side of the Basilica, the Clemenine Chapel occupies the southeast corner of the original centrally-planned layout and consists of a central space covered by a copula and of two small aisles extending north towards the nave and west towards the south transept. The chapel takes its name from Clement VIII, the pope who - for the Jubile of 1600 - commissioned its rich decoration of colored marbles, stuccos and mosaics inspired by the history of salvation and the life of Christ.