1. Boil the chicken breasts in water for about 10-15 minutes. When finished boiling, put in bowl and place in freezer or refrigerator to cool quickly.
2. In blender, blend chicken broth, cream of chicken soup, sour cream, and cilantro together. Add onion, garlic, and peppers until sauce is smooth.
3. Remove chicken from refrigerator. Use a fork to shred the chicken.
4. Brush the tortillas in oil to soften. Spoon shredded chicken into tortilla, top with cheese, and roll tightly.
5. Pour a thin layer of sauce on the bottom of a 9x13 pan. Place rolled enchiladas in pan. Once all enchiladas are in pan, pour sour cream sauce on top. Sprinkle the remaining cheese on top, bake in oven at 350 degrees for about 30 minutes, or until the sauce bubbles and the cheese is melted.