If you have a lot of incoming public and private chat, use the second chat window. By default, you find this as tab button in the main chat:

 

 

You can also open it side by side by either using menu View - Private Chat or by clicking on the button in the menu bar:

 

 

Right click on a chat window (first or second), then call Filter to control which type of chat should be routed into this window.

 

 

Note: These settings will only be stored for the first window if the second chat is visible as extra window pane. Otherwise you might simply overlook incoming chat after restarting the program because it is filtered out in the main window.