Rinse the chicken breasts under cold water and pat dry with paper towels. Trim any visible fat.
Place the chicken breasts in a single layer at the bottom of a medium pot.
Pour in enough filtered water to cover the chicken breasts by approximately 1 inch (2.5cm).
Place the pot over medium heat and bring the water to a gentle boil.
Once boiling, immediately reduce heat to low. The water should barely simmer with only occasional bubbles breaking the surface.
Place the lid on the pot and maintain the gentle simmer for 12-15 minutes for medium chicken breasts.
Use a digital meat thermometer to verify the internal temperature has reached 165°F (74°C) at the thickest part.
Remove pot from heat and allow the chicken to rest in the cooking liquid for 5 minutes.
Remove chicken with slotted spoon or tongs and place on cutting board to cool for 10 minutes before handling.
Once cooled enough to handle, shred the chicken using two forks or slice into appropriate-sized pieces based on your dog's size.