There are two methods for you to close a chat:
Method #1: Hover the mouse pointer over a chat in the chat list and click on the cross.
Method #2: Open a chat and click on the check mark in the upper right corner.
To close a chat from a mobile device use Method #2.
You can configure automatic chat closing when a certain amount of time passes after an operator's response in Settings → General.
To learn more, read the Open and closed chats article.