Mix together dry ingredients in spice mix. Sprinkle spice mix on both side of the chicken breasts. Cook chicken on both sides in olive oil in a saute pan until done. Squeeze lime juice on chicken once cooked and turn off the heat.
Clean out saute pan and cut chicken into small pieces. Drain and rinse black beans and pat dry.
Cook quesadillas one tortilla at a time. Fold tortilla in half, place in saute pan, and open. Sprinkle some cheese on half of the tortilla, then add chicken, then sprinkle in some beans, then add more cheese, and fold the tortilla over so that both halves are surrounding them yummy chicken, bean, and cheese. Place lid on saute pan.
Cook each tortilla covered for about 2 minutes, then carefully flip, replace lid, and cook for about one more minute.
Place each quesadilla on its own plate and top with sour cream and salsa. Cut in half, thirds, or quarters, and enjoy!