This idea has been merged into another idea. To comment or vote on this idea, please visit CUSTCOM-I-234 Delete bulk messages/Conversation in Unified App.
The only way to delete a chat is one-by-one. The entire string of the conversation can not be deleted. Also, I cannot delete the senders chat note, only the ones I sent. I tried exporting the conversation to a folder and then deleted the folder, but it only deletes the folder not the underlying conversation. This seems like a major flaw in the program.