Thank you for your votes and comments on this feature. The team is in the process of finalizing designs for deleting private chat threads. I will update as we have more progress to share.
An error occurred while saving the commentPeter commented
While I would also like to delete chats, some of the commenters who mention being able to delete chats in other applications seem to be unaware of the permanence of electronic communication. Microsoft has chosen to make Teams transparent in this manner. If a user sends communication, that user will always be able to access it since whichever server is hosting it will always be able to access it. "Deleting" the communication in most other apps is really only hiding it without the ability for the user to ever get it back.
For those who are simply looking to clean up their communication, hiding is what accomplishes this. Hiding can be made better by allowing the user to hide portions of any given conversation.