2 question about chat-room:
Can one delete own comment in chatroom?
Can owner of chat-room delete chat-room?
The links given by Martin Sleziak answer both questions.
Room owners cannot delete the room. Rooms are frozen automatically after 15 days of inactivity; a frozen room with few messages is subsequently deleted. See How do you delete a room on chat.
A user can delete a chat message only during 2 minutes after it was posted. If there is a good reason for the message to be deleted, the user should either (i) ping a moderator, or (ii) flag for moderator attention. Generally, (i) is preferable to (ii) because flags propagate across all Stack Exchange chat rooms (except those attached to SO and meta.SE) which gives your request a bit more publicity than you wanted. Room owners cannot delete messages, but they can move them to another room. See: Allow owner of message to delete them in chat.