Updated September 11, 2013, see below.
Both Kingdom Hearts III and Kingdom Hearts χ[chi] have been confirmed to appear at Tokyo Game Show 2013, via a press release uploaded to the official TGS website. Tokyo Game Show 2013 runs from September 19 to 22, 2013. At E3 2013, series director Tetsuya Nomura implied that new Kingdom Hearts III information would be released at the event.
Update 1: Square Enix have launched their official Tokyo Game Show 2013 website. Currently, the website covers various Square Enix titles appearing at the event, including Kingdom Hearts χ[chi]. A page for Kingdom Hearts χ[chi] is available, containing some screenshots from the game. Stay tuned for more info.
Update 2: Square Enix have listed some merchandise which will be available at Tokyo Game Show 2013. Available for the first time is the Kingdom Hearts keychain set, pictured here. Amazon.co.jp have also listed this 6-keychain box, which is set for a release date of October 4, 2013 for a price of ￥3,215 (approximately $32.12).
Update 3: Square Enix have released their booth map for Tokyo Game Show 2013. This confirms that there will be an "Open Mega Theatre", which means it is likely that all trailers shown will be available for everyone to see (and secretly record). You can see this below.