Preheat your grill to medium-high heat (about 400°F).
In a small bowl, mix together the garlic powder, onion powder, smoked paprika, salt, and black pepper. Rub this spice mixture evenly over both sides of the chicken breasts.
Place the chicken on the grill and cook for about 6-7 minutes on each side, or until the internal temperature reaches 165°F.
During the last few minutes of grilling, spoon salsa verde over each chicken breast and top with shredded pepper jack cheese. Close the grill lid to melt the cheese, about 2-3 minutes.
Remove the chicken from the grill and let it rest for 5 minutes. Garnish with fresh cilantro, if desired, and serve with lime wedges.