A good news! You can backup your chat logs in Gmail now with Gmail Keeper!
To do that, the first step is to enable IMAP access for your chats (this was not possible not long ago), illustrated in the following screenshot.
Then, in the backup settings window in Gmail Keeper, you must set ‘Chats‘ is a ‘Label’ when being asked, as shown in the following screenshot.
And the backed up gmail chats will be stored in eml format just like the ordinary emails. Check the screenshot below to have a look how the chat logs look like in the free Thunderbird email client program.
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