You can display the current number of unread chats in your browser icon.
Login to Chatwork and click [ Your name ] → [ Personal Settings ] → [ Display ] tab on the upper right corner of the screen.
Check the "Show unread numbers on browser icon" on the "Display" and click the "save" button at the bottom of the screen.
The number of unread chats will be displayed in your browser icon.
Below shows the browser "Google Chrome" with "4" unread chats.