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Brush the chicken breasts with olive oil and sprinkle with salt and pepper. Lay the chicken on a grill over medium heat (you can hold you hand 1 or 2 inches 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).
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Slice the cooked chicken breasts into 1/4 in.-thick slices. Keep grill or grill pan hot.
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In a small bowl, whisk together the chipotle chile, sour cream, mayonnaise, lime juice, and cilantro.
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Spread 1 tablespoon 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).
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Put each quesadilla on a dinner plate.
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Slide the 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 tortillas in batches).
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Grill uncovered turning once, until the cheese is melted and both sides are golden, about 2 minutes each side (use a large spatula and tongs to flip the quesadillas).
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If grilling in batches, keep finished quesadillas warm in a 200 degree oven until ready to serve.
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Slice each quesadilla into wedges and serve with salsa on the side.