The ancient basilica of Old St. Peter's in what is today Vatican City was one of the earliest churches built by the Byzantine
Emperor Constantine during the early Christian period in the 4th century AD. The site was originally the location of Nero's Circus and part of the Roman Empire
; Constantine began his replacement structure in 324. Said to have been built over the grave of Peter, one of the disciples of Christ, the building's cross-shaped plan was echoed by other smaller churches throughout the Roman empire. It was replaced by the current structure, New St. Peter's, which was built between 1506 and 1615.
In 1950 Pope Pius XII announced that archaeological excavations had discovered the tomb of St. Peter himself under the altar. Excavations were overseen by Monsignor Ludwig Kaas who wasn't the most sympathetic to archaeological aims, however; and the bones were probably too young to represent "the rock" upon which the church was built.
An old news story about the search for St. Peter's tomb hangs around on the web at the Catholic Education
website. More on the basilica herself maybe found at the official St. Peter's Basilica homepage