Can you view your previous chat history with a friend on Facebook?
You can view recent conversation history by opening a chat window with your friend. At this time, you cannot view older conversations or conversations with friends who are not currently online.
[Source - Facebook Help -> Chat: How to use the Chat feature and privacy -> How do I delete or look through my Chat History? Is it saved permanently? ]
Not if you are just using the base chat within Facebook. There is an app that claims to do it but I don't think it is very reliable. (I haven't tried it myself though). If you use another client to do Facebook chat such as Trillian or Pidgin or anything that supports Facebook chat, those clients may have the ability to log conversations.