In medium bowl, whisk taco seasoning, oil, vinegar, water, juice of lime and pepper. Place chicken breast halves into a large ziploc storage bag and pour marinade over the chicken. Seal the bag and work the marinade around until the chicken is evenly coated.
Refrigerate at least 3 hours.
Preheat the grill to 350°F.
Place the whole peppers on preheated medium grill and cook until blackened on all sides. Remove from the heat and immediately place in a plastic bag to let the peppers sweat for 20 minutes. After 20 minutes, remove the peppers and the skin should easily peel off of each one. When peeled, slice in half and clean out the seeds. Set aside.
Cook chicken on medium grill for 5 minutes on each side chicken has reached internal temp of at least 165°F. Lay one pepper slice on each chicken breast and cover with cheese. Cook over low heat with the lid closed until the cheese melts. Place on a serving plate, cover with foil and let rest 5 minutes.
To serve, garnish with pico de gallo and sour cream.