Season both sides of the chicken breasts with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat.
Add the chicken breasts to the skillet and cook for 5-6 minutes on each side, or until golden brown and cooked through (internal temperature should reach 165°F).
Remove the chicken from the skillet and set aside on a plate.
Reduce heat to medium and pour the salsa verde and chicken broth into the skillet.
Stir to combine and bring the sauce to a simmer.
Return the chicken breasts to the skillet, spoon some sauce over the top, and simmer for 5 minutes to allow the flavors to meld.
Sprinkle chopped cilantro over the chicken.
Serve the Salsa Verde Chicken hot with lime wedges on the side.