Hi,
There are two things that are going on here.
1) Is Lion's ability to open a window that was Open on Shut down.
This can be added to by iChat own ability to re-open Chats that were Open on Quit (It could do this before ichat 6)
2) The second is which .plist is holding the Recents List
com.apple.iChat.LSSharedFileList.plist also holds the info in the Recent Chats List.
Recent Chats can also be changed by System Preferences > General Pane and the Setting for Documents.
This goes across all apps (or servers or Applications) which is why the .plist has a "Shared" name.
The Chat is probably "Staying" as you are not saying you are Closing that window (the red blob only close windows in iChat)
There is a third possibility and that is for some reason that one chat (The first "Day" probably) was added to System Preferences > Accounts > (Your account) Login Item list.
I hope this gives you some ideas.
A) the chat is the only bit made on the startt day of the chat (May have been the only bit during an iChat Session)
B) It may be that window is not Closed before iChat is Quit or computer Shut Down happens so it is being "brought" back.
C) Possibly it (the chat) is listed as a Login Item.
11:20 PM Sunday; February 5, 2012
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.3)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
"Limit the Logs to the Bits above Binary Images." No, Seriously