Assuming that your admin has not turned off the permission, you can follow these instructions:
Note: Messages or files are not immediately removed from the view of people who have already joined the room. The next time they sign in, they will no longer see the message.
This is an excerpt from https://confluence.atlassian.com/hipchat/delete-messages-and-files-751698289.html. There are instructions on how to delete from 1:1 chats there also.
Hope it helps!
...have mention name FirstnameLastname. Fe.: @MaartenCautreels This certainly helps to know who is being mentioned in a conversation. Imagine your colleague sends the following message...
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