Cut 1/2 inch from the top of each pepper and reserve the tops. Remove the membranes and seeds from the body and blanch the peppers in boiling water for 30 seconds. Remove from the water, drain and cool.
Season the chicken breasts with salt and pepper. Brush them with oil and grill until done. Cool the chicken breasts and slice them into thin strips.
Preheat the oven to 375°F. Combine the chicken, cream cheese and 1 1/4 cups of the salsa in a food processor. Season with salt and pepper and pulse, mixing well but being careful not to puree.
Fill the peppers with the chicken mixture and replace the tops. Place the peppers in a baking dish and cover with the remaining salsa and shredded cheese. Bake for approximately 30 minutes, or until hot throughout.