Stavrogins Confession

The chapter you're referring to, entitled "At Tikhon's", was originally in Part 2, Chapter 9 of "Demons". Many versions printed now either include it at that place, or as an appendix at the back of the book. This is the explanation offered in the introduction to my version by Joseph Frank:

"A good part of 'Demons' was published in installments during 1871, despite the disturbance caused by the Dostoevskys' return to Russia in July (the manuscripts of 'The Idiot', 'The Eternal Husband' and the early drafts of 'Demons' were all burned for fear of running into trouble at the border). But publication stopped after the NOvember issue, when Part 1 and eight chapters of Part 2 had already appeared, and did not resume until almost a year later. The reason was that, in what was intended as chapter 9 of Part 2, Dostoevsky describes a visit by Stavrogin, assailed by hallucinations of various mocking 'devils', to a nearby monastery to seek for spiritual aid from the monk Tikhon. This name and character come from an eighteenth-century saint whom Dostoevsky admired, St. Tikhon Zadonsky, who plays an important role in 'The Life of a Great Sinner' and has been taken over from there (he later also provided inspiration for Father Zosima in 'The Brothers Karamazov'). Stavrogin asks Tikhon to read a confession in which he describes his seduction of a twelve-year-old girl, whose suicide he then does nothing to prevent. Dostoevsky was told that Katkov would not print this chapter, but no final decision was taken on its exclusion until just before the November issue of 1872.
"Meanwhile Dostoevsky made attempts at revision which left the question of an actual rape uncertain, hoping this would be enough to satisfy 'the modesty' of his editors; he also read this chapter to his literary friends to obtain their advice (which later led to ugly and totally unfounded rumors, handed down to posterity, that he was actually confessing a misdeed of his own). Continuing to forge ahead with the remainder of the book, he wrote on the assumption that his contested chapter would be accepted in its revised form; but publication continued to be delayed. It was only a year later, just before publication resumed, that he received a definitive refusal, and he then worked frantically on the galleys to give his remaining text whatever coherence he could.
"One addition, made at the last moment to the original manuscript of Part 3, is of some importance - the scene in which the dying Stepan Trofimovich listens to the reading of a passage from St. Luke (Dostoevsky also uses this passage as epigraph), about the devils entering into a herd of swine and drowning in the sea. It is under the inspiration of this passage from the Gospels that the repentant Westernizer declares himself to be one of the devils, and perhaps their progenitor. It is possible that, if Dostoevsky's initial Chapter 9 had been accepted, he would have assigned more responsibility to Stavrogin, whose social-cultural coloration makes HIM the far more plausible (and historically accurate) source of Dostoevsky's ideological devils. The original plot assignment of Stepan Trofimovich as Stavrogin's tutor, who is thus presumably the cause of all the moral-ideological maladies of his pupil, is obviously a structural hangover from the earlier plan before the Prince had been transformed into Stavrogin and taken over the book.
"However that may be, chapter 9 vanished among Dostoevsky's papers and was only unearthed in 1922, although parts of it (the dream of a Golden Age of innocence, mirrored by a classical Greek landscape taken from Claude Lorrain's 'Acis and Galatea') were used in 'A Raw Youth'. There has been a continual dispute over whether it still belongs to the book, but the consensus is that it should certainly be read if we are to grasp the moral-philosophical inspiration underlying Dostoevsky's remarkable character. ..."

That, again, is from Joseph Frank's introduction to the Everyman Library edition of "Demons". Sorry for the long quote, but I felt that he could probably explain it a little better than I could. Hope it helps.