Brush chicken breasts with olive oil and sprinkle with salt and pepper.
Lay chicken on a grill over medium heat (you can hold your hand 1 to 2 in. above grill level only 4 to 5 seconds) or put chicken in a grill pan over medium heat. Cook chicken 4 to 5 minutes per side, or until cooked through (cut to check). Slice cooked chicken breasts into 1/4-in.-thick slices. Keep grill or grill pan hot.
In a small bowl, whisk together chipotle chile, sour cream, mayonnaise, lime juice, and cilantro.
Spread 1 tbsp. chipotle-lime sauce on each of the tortillas. Top 4 of the tortillas each with 1/2 cup cheese and a quarter of the chicken slices, then cover with the remaining tortillas (sauce side down). Put each quesadilla on a dinner plate.
Slide quesadillas off the plates onto the grill over medium heat, or slide into a grill pan over medium heat (you may need to grill the quesadillas in batches). Grill uncovered, turning once, until cheese is melted and both sides are golden, about 2 minutes each side (use a large spatula and tongs to flip the quesadillas). If grilling in batches, keep finished quesadillas warm in a 200 oven until ready to serve.
Slice each quesadilla into wedges and serve with salsa on the side.
Cheeses: Try shredded Monterey jack, cheddar, or goat cheese.
Meats and seafood: Set out platters of grilled chicken, steak slices, bacon, and cooked shrimp.
Vegetables: Round it out with canned black or pinto beans (rinsed and drained); grilled corn, peppers, summer squash, zucchini, and onions; and sliced fresh green onions.
Serve with the chipotle-lime sauce, pico de gallo, guacamole, and sour cream.
