chats are saved as temporary internet files, which get cleared out quite often. However within 24 hours if the same person comes online you should be able to see what you talked to them about the previous day.
Facebook stores a lot of information; profiles, pictures, videos, and music, all of which are backed up daily. Due to the amount of users on facebook and the amount of chats being sent each day there just isn't enough room for us to back up this kind of information.
If you want this to be a feature I would recommend contacting the facebook developement team and asking them to add an enhancement for you to be able to do this. Although it has been suggested before and it is not currently being worked on, mainly due to the need to increase server capacity.
So to answer your question at this time the chat data is only temporarily saved for a very short period of time, more than likely the conversation you are looking for is long gone by now.
