[Lillith]

Yup, you have to keep food off the counter when you aren't there to supervise. It also helps to block access to the kitchen or teach the dog a "place" command when you're in the kitchen to completely eliminate all opportunities to grab food and self-reward. Or, when you have to leave the room, take the dog with you and reward him for following you and not going in the kitchen to grab stuff.

I also found that rewarding heavily for keeping feet on the ground in the kitchen helps. I would give my dog little scraps of what I was cooking, but I would only deliver the reward in his food bowl, or on his bed.

 

[Lillith]

It's not food. Its everything else, wallet, paper towels, etc. Hes only chewed the wallet. Everything else he just hides in his little corner.

Same idea. Keep stuff off the counter. Make sure he has plenty of chews on the ground. I imagine this behavior will go away as he matures, but until then you simply must eliminate the opportunity to steal.