To cook chicken for puppies, select a skinless, boneless chicken breast, which is lean and easy to shred. Rinse the chicken under cool water and place it in a pot, then add enough water to cover the chicken. Bring the water to a boil over medium heat, then reduce the heat and let it simmer until the chicken is cooked through, which usually takes about 12 minutes for medium-sized chicken breasts. Make sure the chicken is thoroughly cooked and no longer pink in the middle. Once cooked, remove the chicken from the pot and let it cool before chopping or shredding it.