When hovering over a specific message, display buttons / links / menu for posting the content to specific social networks, such as Facebook or Twitter. Store (and, perhaps, display) metrics on how many times each message has been forwarded to each network; these metrics could be used to weight search results (if two messages contain the same search term[s], but one has been tweeted 80 times and the other one hasn't been shared at all, it's likely that the former is more interesting, if not necessarily more useful).
These buttons should only display in chats marked as public or moderated.