Combine the chicken broth and chicken breast in a large pot over medium-high heat. Once the broth boils, drop the heat to medium-low and let it simmer gently for 20 minutes or until the chicken is thoroughly cooked. Test for doneness by making a cut in the thickest part of the breast.If the juices run clear, the breast is ready.nce the broth boils, drop the heat to medium-low and let it simmer gently for 20 minutes or until the chicken is thoroughly cooked. Test for doneness by making a cut in the thickest part of the breast. If the juices run clear, the breast is ready.