A chat message can be edited or deleted up to 1 hour after it has been sent. To do this, click on the three dots on the desktop when you hover over your message and then select "Edit" or "Delete" (the message is then deleted for everyone).
On the smartphone, you can hold your finger on the message for a second so that the selection for editing and deleting appears.
To delete a private chat completely, click on the three dots at the top right of the chat and select "Delete chat". However, it will remain for the other person.