I sent a message to someone that I didn't mean to, although they haven't seen it yet. It was very personal and I don't want them to read it. Is this possible to accomplish?
There is no way of deleting your message from your friend's Chat Inbox or from a Conversation once it is sent. Messages will only be deleted from your Chat Inbox or Conversation.
The official article from Facebook Help Center:
How do I delete messages or a conversation?
You can delete messages one at a time, or you can delete an entire conversation.
Note: Once you choose to delete a conversation, this can't be undone.
Keep in mind that deleting a message or conversation from your inbox won't delete it from your friend's inbox. It isn't possible to delete sent or received messages from a friend's inbox.