At the end of movie, Dr Lecter calls Clarice at her convocation day at FBI. From which place does he call Clarice? And how did he know that Dr. Chilton was going to be there? What makes him follow Dr Chilton?
Lecter and Chilton are both in Bimini in the Bahamas which is where Hannibal calls Clarice from. It is unclear how he knew that Chilton was going to be there. But presumably, Lecter could have simply called his office and been informed that he was (going to be) on vacation in the Bahamas.
Lecter follows Chilton because of the treatment meted out to him in the latter's Baltimore asylum. He also considers Chilton to be rude and uncouth and Lecter doesn't like rude people:
The closing, where Hannibal says: "I'm having an old friend for dinner" as he watches Dr. Chilton deplane, strongly suggests that Chilton ended up as one of Hannibal's meals. A small reference was made in the sequel novel Hannibal, where it was mentioned that Chilton disappeared seven years earlier while on vacation, strongly suggesting Hannibal had gotten his revenge (albeit in the novel, Chilton disappeared in Jamaica, not the Bahamas). However, this is never specifically stated in the sequel movie. The only reference to Dr. Chilton in Hannibal is made by Barney, when he says that Lecter, when possible, preferred to eat "the rude," and Dr. Chilton "was a bad man," which also strongly implies Chilton became Hannibal's victim.
I believe in two theories that are similar and not similar in both ways. We know that during Chilton's arrival in the Bahamas, Lector followed on that one street. What if Chilton knew he was following him? By saying this, this theory is saying that Chilton and Lector are somehow someway working together. Some evidence toward this is when Clarice takes yet another visit to Lector's cell when Chilton stops and argues with her the reasons (which are classified by the FBI) why she is there for another visit. He was very angry and nervous-looking making some presume that Chilton doesn't want Clarice to find him out. The second piece of evidence for that theory is when Chilton is lying on the ground frustrated toward Lector in the new cell he got at the new jail destination which could be a tactic which makes it seem as if he is actually angry. The next theory is that Lector has vengeance due toward Chilton after years of torture and hate.
I believe Chilton's arrival was due to machinations set in play by Dr. Lecter himself. A ruse employed by Dr. Lecter giving Chilton both, a soon-to-prove-fatal ego trip that his name (Chilton's), will once again presently be in the spotlight as the handler of Dr. Lecter (as the only man with the insight in to Lecter's unique mind to be able to track him and bring him down), and secondly as an assuredly, 'most horrible wake up call imaginable' pending (Chilton is clearly a raving Knob.). When the two inevitably cross paths the ball can only, without a doubt, be in Lecter's court (Chilton's back alley muscle, (-'We have the top-notch security'- good for you matey ;) for shame certainly no match for the driving force that is Lecter :)