ST. PETER'S  San Pietro in Vaticano

Kempe does not mention going to St. Peterís specifically, but it would be inconceivable that she did not.  If she visited San Giovanni in Laterano and Santa Maria Maggiore, she probably visited all of the seven major basilicas in Rome. St. Peterís basilica is built over the grave of St. Peter (died c. 64 AD) the leader of the Apostles, and first pope.  Kempe also uses St. Peter's as metaphor of safety: Christ promises her that she and her companions will be as safe as if they were in St. Peter's Church: Ch. 42 Than owr Lord Jhesu Crist seyd to hir mende, "Drede the not, dowtyr, for thu and alle that ben in thy cumpany schal gon as safe as yyf thei wer in Seynt Petrys Cherch."  

Begun c. 319-22 by the Emperor Constantine, it was one of the largest buildings in the world and the most important pilgrim shrine in Europe.  After the popes of Avignon returned to Rome in 1377, they made the Vatican hill and St. Peterís their place of residence, though the basilica of St. John Lateran remained the popeís official seat in Rome. During the latter Middle Ages, especially during the 14th century when the popes were either absent from Rome or challenged by anti-popes, the Early Christian building that consisted of a very long nave and open atrium fell into disrepair.  This is the church visited by Margery Kempe. 

The present building dates from the complete reconstruction begun by Pope Julius II in 1506.  Old St. Peter's was leveled and new plans, altered several times during construction, were drawn up in the Renaissance style.  Ultimately a centrally-planned church (designed by Bramante and Michelangelo) was extended into a Latin cross to occupy roughly the same space as the original basilica.  The addition of Bernini's great colonnade in the mid 17th century further enhanced the site by monumentalizing the square itself.

Margery Kempe would have been primarily interested in the great wealth of relics and accompanying indulgences available to the faithful visiting St. Peter's. The veil of St. Veronica, believed to have been imprinted with the image of Christ when he wiped his face just before his death, was one of the most venerated.  John Capgrave (Ye Solace of Pilgrimes: A Description of Rome circa A.D. 1450 by John Capgrave, an Austin Friar of King's Lynn, ed. C. A. Milles, London: Oxford University Press, 1911, 63-64) calls the image the Vernacle and devotes considerable space to its description.  He notes the aged look of the image because of the extreme suffering of Christ.  Brewyn described the indulgences available when the relic was shown: 

Also whensoever the face of our Lord Jesus Christ is shown there are three thousand years of indulgences, that is to say, those who live near Rome have six thousand years of indulgences, and those who come over the mountains and hills have nine thousand years of indulgences, and as many quarantines, and the remission of a third part of all sins (William Brewyn, A Fifteenth Century Guidebook to the Principal Churches of Rome, trans. C. Eveleigh  Woodruff, London: Marshall Press, 8). 
Images now are the only ways to picture the original 4th century basilica as Kempe would have seen it. Certain interior furnishing still remain: the bronze statue of St. Peter, once attributed to Arnolfo di Cambio (c.1300), and located in the nave; and the marble spiral columns that were part of the original presbytery, both mentioned by Brewyn.  The columns were repositioned to the reliquary balconies in the four piers of the rebuilt Basilica.  The extended foot of St. Peter is traditionally rubbed by pilgrims visting the church, Kempe may have done so as well. In Kempeís day Giottoís famous mosaic of the Navicella (Christ Calming the Sea) was also in Old St. Peterís. It no longer exists, but there are reconstruction drawings of it. Medieval pilgrimage guides note the columns and the statue.
  •  In the church of St. Peter . . . there are a number of columns of white marble marvelously carved to represent, as it were vines with leaves and clusters of grapes, running up the pillars, beneath one of which, it is said, Jesus sat when He was preaching in Solomon's temple at Jerusalem whence it was brought to Rome, and is now well protected with iron, and almost every day it works great virtues, especially on demented persons, and on those possessed by devils.  A priest is often in attendance with a book, who, vested in surplice and stole, is ready to help inform folk by prayers, etc.   (Brewyn, 33-34; See also Capgrave, 65)
  •  Also there is in the church a great image of St Peter of cast metal (Brewyn, 33-34).