Like in other messenger apps, you can hide chats that you no longer want to see in your general list of chats anymore. The chats can then be found in a separate section with all other hidden chats and will only appear outside of hiding if you want them to. So even if messages are sent within the hidden chat they will not bother you.

To hide a chat on the desktop or browser version of Zenchat make a right click on the desired 1:1, topic chat or group chat and select "Hide". 

As soon as you have clicked "Hide" the chat will no longer be visible with your other chats. In addition to that you won't be receiving any notifications regarding hidden chats. To access hidden chats simply click the little eye symbol on the right side of the search bar. 

This will lead you to a collection of all hidden chats. New messages that are being sent into hidden chats will not cause the chat to reappear. To Make a chat reappear, open your hidden chats (the eye symbol should be green) and right-click on your desired chat again. But instead of "Hide" click "Show" now. 

This will bring the chat back to the general collection of all chats. And will cause you to see any actions made within the chats. 

To hide and show chats on a mobile device just swipe from right to left on your desired chat. An eye will appear. Click on it to either hide or show the corresponding chat.