Root 17, I am not 100% sure, and if I am incorrect, someone will come along and correct me.

That final scene that you mention above, when Lecter speaks with Clarice and says "I'm having an old friend for dinner", and you see Chilton getting off the plane...well this is why that came about:
Remember when Lecter killed the cop in Texas and everyone thought Lecter was the fallen officer? Lecter escaped and a massive manhunt ensued.
Now skip to the final scene when Lecter is speaking with Clarice...what you wouldn't know if you didn't read the book, is that since Lecter is on the lamb

(no pun intended), he heads to the Carribean, however, he assaults a tourist there, and eats the tourist's vocal cords, and steals his identification, money and wallet.
So naturally, since Chilton is listed as Lecter's doctor, they would contact him and the police stateside. That is how Doctor Chilton ended up on the same island...I think.
