Sorry to hear that - I can imagine how frustrating it must be! Whether or not you can recover your conversation really depends on what chat program you were using, and if you had the archive feature enabled.
What Chat Programs Support Conversation Archiving?
- Windows Live Messenger (MSN)
- Yahoo Messenger (YIM)
- AIM (AOL Instant Messenger)
- Facebook Chat
What Else Can I Do To Retrieve My Conversation?
Well, you could always ask the person that you were talking to - it's possible that they saved it themselves, or didn't close the window, and could copy-and-paste or save and send the file to you.
Hope you manage to recover your conversation, and be more careful in the future!