Just stop using the room. It'll be deleted or frozen (depending on how much it was used) automatically after either 7 or 14 days.
See the Chat FAQ:
Rooms will exist indefinitely, so long as there is at least one person actively talking in the room. A room is considered worth retaining if it has more than 15 messages by at least 2 users.
Rooms not worth retaining which are inactive for 7 days will be deleted. Rooms worth retaining which are inactive for 14 days will be frozen. Frozen rooms do not allow any new messages to be sent, and are not shown in the default room list to prevent cluttering the rooms interface.
Note that 3 of the rooms you created on chat.stackoverflow.com have fewer than 15 messages in them, those will all be deleted in 7 days time if you don't add any more messages to them. The 4th one will be frozen in 14 days time; there are more than 15 messages by 2 people in that room.
You can always switch the room access level to 'Gallery' (room info -> Access tab) to prevent people from talking in a room you want to see frozen or deleted.
There is no option available for explicitly deleting a room. Don't use Stack Exchange chat rooms for conversations that you expect to be private.