Two years ago, I planted a weeping peach tree. Last spring, Kendra chewed all the bark off the bottom foot of it. It survived until the summer heat got to it. I pulled it up, in preperation to throw it away. It was about an inch thick and 5' long. The next time I looked the dogs was fighting over the stick. They finally layed down and chewed on opposite ends of it. Now, 5 months later it's still in the yard, and get chewed on a bit every day.
I was curious about that stick, and after a week on so, I washed off a spot and chewed on if for a second. It didn't really have a taste, but it did have a peachy aroma. So, go claim a branch or two for you and Chip. I bet it's good!