To make salsa, in a bowl, mix apple, onion, bell pepper, cilantro, apple juice, vinegar, and chili. Cover and chill.
Rinse chicken and pat dry. Rub chili spice mix all over chicken.
To grill, coat both sides of chicken breasts lightly with olive oil and lay on a grill over medium-high coals or medium-high heat on a gas grill (you can hold your hand at grill level only 3 to 4 seconds); close lid if using gas. Cook, turning once, until chicken is no longer pink in center of thickest part (cut to test), 6 to 8 minutes total.
To sauté, set a 10- to 12-inch nonstick frying pan over medium heat. When pan is hot, add oil and tilt to coat bottom. Lay chicken breasts, slightly apart, in pan (if using a 10-inch pan, cook chicken in two batches, using half the oil at a time; keep cooked breasts warm, lightly covered, in 200° oven). Cook, turning once, until chicken is no longer pink in center of thickest part (cut to test), 10 to 12 minutes total; reduce heat slightly if chicken begins to brown excessively.
Transfer chicken to plates. Serve with green apple-chipotle salsa.
Chili spice mix: In a small bowl, mix 1 tablespoon paprika, 1 teaspoon each salt and pepper, 1/2 teaspoon chili powder, 1/2 teaspoon firmly packed brown sugar, and 1/8 teaspoon cayenne.