I had the same problem. I went to Google play and updated the app and so far have not had problems. Hope it helps, I was ready to go elsewhere to play.
Ads while playing on phone (Android)

I also had fullscreen ads every 10 seconds while playing and uninstalled it. Fullscreen ads during a game, whether every 10 seconds or minutes, is unplayable.

@An_8x8_Battle- Sorry you're getting so many ads! We did fix the issue so if you'd like please try reinstalling the app and you should be set. If you reinstall and you're still getting an overabundance, please let me know.

I appreciate the responses. I ended up doing what t_taylor recommended and that fixed the issue immediatly. Thanks.

Thanks, jac1yn. I'll try redownloading it.
It's a Kindle Fire, so I don't have access to Google Play for t_taylor's solution. I don't want to take the chance to brick it, so I'm keeping it stock.

jac1yn, yeah, it's still happening. I started a game with a computer as a guest, and it popped up with a fullscreen ad five moves in.
It looks like the version available for the Kindle Fire isn't the most recent version:
Google Play v2.0.34
https://play.google.com/store/apps/details?id=com.chess&hl=en
Kindle Fire v2.0.26
http://www.amazon.com/Chess-com-Chess-Play-Learn/dp/B005XDGT9U
I've been using my android to play live games for the past month or so and haven't experienced any pop up ads until tonight. I would understand one coming up every 10 minutes or so, but these popped up literally every 10 seconds, during an entire game. They we're mostly for Candy Crush and that dumb Pet Rescue game, but some ads came up for Amazon as well. Is this something that was newly implemented? If so, dear god. I hope not. I understand wanting to gain paid customers but this isn't the way to do it.