How do I clear my Recent conversations in Skype for Mac OS X?
You can clear all Recent conversations from the sidebar, or remove individual conversations. This does not permanently delete conversations; they will still be available in your history.
To remove all Recent conversations from the sidebar, go to the main menu bar, click Conversations, then click Clear Recent…
You will need to remove a conversation from Favorites before it can be removed from the sidebar. To remove a conversation from Favorites, CTRL-click the conversation in the Favorites section, then click Remove from Favorites.
Then, to remove a single conversation from the sidebar, go to the sidebar and CTRL-click the conversation you want to remove, then click Close.