Heat olive oil in a large skillet over medium-high heat.
Add peppers and onion and cook over high heat, until starting to brown, about 5 minutes. Transfer peppers and onion to a bowl and set aside.
Season chicken breasts with salt and pepper. Place chicken breasts in same skillet and cook 4-5 minutes per side, till browned.
Pour salsa verde, chicken broth, and remaining spices over chicken breasts. Lower heat to medium, cover skillet, and let simmer 15 minutes or until chicken is cooked through.
Remove chicken breasts from skillet and shred.
Return shredded chicken to skilet with peppers and onions. Stir in lime juice and cilantro.