Nope. Once its deleted, its deleted. Unless you just archive it. If you archived it, then you just search the person that you wanted to see the conversation of & click on messages , then all the archived messages pop up. Not the deleted ones.
It is not possible to recover your deleted chat conversation once you delete it from Facebook. Facebook does not have the capacity to have you recover any of your information or messages that you delete. You could only trace the chat conversation if you archived it, where you search the name of the person you chatted with and click the message icon to find the conversation you previously had.