Preheat the oven to 175°C (350°F). Cover a baking sheet with baking paper and set aside.
In a medium bowl, combine shredded chicken with oil and stock. For a finer texture, you can blend the chicken with stock prior to adding oil.
Add flour and polenta and mix until it's all combined and resembles a dough. Flour your work surface and roll out the dough to 1/4 to 1/2 inch thick (about 0.5-1 cm thick).
Cut out your treats in any desired shape and place them on the baking sheet. They can be placed close together, as they won't get bigger during baking. Bake for 20 minutes in the center of the oven. Let them cool for about 10-15 minutes before serving.
Notes
If cooking fresh chicken breast, cook it in water in a pot covered with a lid. Once the chicken is fork-tender, remove the pot from heat and allow it to cool before using. While this recipe uses chicken breast, you could experiment with darker meat such as chicken thighs. You can use the water you cooked the chicken in instead of chicken stock.