In a medium bowl, stir together the biscuit mix and milk just until it pulls together. Set aside.
Pour the cans of chicken broth into a saucepan along with the chicken; bring to a boil. Once the broth is at a steady boil, take a handful of biscuit dough and flatten it in your hand. Tear off 1 to 2 inch pieces and drop them into the boiling broth. Make sure they are fully immersed at least for a moment. Once all of the dough is in the pot, carefully stir so that the newest dough clumps get covered by the broth. Cover, and simmer over medium heat for about 10 minutes, stirring occasionally.