Hide private chat tab show when needed
Hide private chat tab, show when new messages come in
In the Chat Window itself, there should be a "Hide" button.
Scenario: You are having a private (or group) chat. The Chat is "over" and there is no reason to keep it in your "Recents" since the topic was transient/time sensitive only. You should be able to "Hide" (Close) the chat right from the Chat window. Do not make the user click multiple times to get back to "Recents", then find the Chat, click again to get the option to Hide and then have to click "Hide".
Unnecessary clicks reduce productivity, reduction in productivity is an increase in expense which reduces overall company profits.