It is supposed that at some point in Vatican history an event took place commonly referred to as the banquet of chestnuts. However this story is doubted and discounted in many quarters. Is there any archival evidence which may allow one to study this occurrence further?
Generally speaking, orgies do not leave archival evidence.
The major source for the Banquet of Chestnuts is a diary entry from Johann Burchard. It reads:
On the evening of the last day of October, 1501, Cesare Borgia arranged a banquet in his chambers in the Vatican with "fifty honest prostitutes", called courtesans, who danced after dinner with the attendants and others who were present, at first in their garments, then naked. After dinner the candelabra with the burning candles were taken from the tables and placed on the floor, and chestnuts were strewn around, which the naked courtesans picked up, creeping on hands and knees between the chandeliers, while the Pope, Cesare, and his sister Lucretia looked on. Finally, prizes were announced for those who could perform the act most often with the courtesans, such as tunics of silk, shoes, barrets, and other things.
Vatican researcher Peter de Roo spent years in the archives trying to rehabilitate the image of the Borgias. The five volumes of evidence he collected can be seen here. Wanting to disprove the Banquet, apparently the closest de Roo came to a smoking gun was a passage from the Chronicle of Mattarazo and a letter to Silvio Savelli. From the Chronicle, we have mention of a feast attended by ladies and gentlemen of the court. According to de Roo, the letter "states only that the courtesans were invited to eat at the palace and offered a most shocking sight. It notices no further particulars nor the presence of any of the Borgias."
So it is de Roo's belief that the account found in Burchard's diary (clearly secondhand--and de Roo at least thinks it was written by someone other than Burchard) is an interpolation of several milder events that, when combined and exaggerated, make for a very salacious story.
So did the Banquet of Chestnuts happen? Well, it's hard to prove a negative. But de Roo found nothing incriminating, and he was undoubtedly thorough. There is the question of de Roo's objectivity as a Vatican researcher invested in rehabilitating Alexander VI, but still, it seems like most historians at least have doubts regarding more extreme takes on the Banquet.
As an aside, one historian who does not seem to have doubts is William Manchester. Note that many on this site do not take A World Lit Only By Fire to be a credible source. Apparently, the Banquet of Chestnuts is further confirmation that William Manchester is not to be trusted.