Never mind, I found it:
http://www.chess.com/download/view/chesscom-for-android-phones--devices
Resolved: Latest Android chess
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Just got a Kindle Fire and I need a direct link to an apk to install it - without jailbreaking the Android Market is off-limits. I got one from chess-3.com but that looks like a release candidate.
Where can I find the latest apk for Chess.com Android? And once installed, will it automatically stay up-to-date?