Combine 1/4 c water, cliantro, sliced jalapeno, lime juice and olive oil in blender. Blend until smooth. Season to taste with salt and pepper. Place chicken in shallow baking dish. Pour marinade over, coating completely. Cover and refrigerate 4 hours. Preheat broiler. Remove chicken from marinade; discard marinade. Broil chicken until cooked through, about 3 mintues per side. Set chicken aside. Lightly brush both sides of onion and eggplant slices with vegetable oil. Sprinkle both sides with salt and pepper. Broil vegetables until tender and golden, about 2 mintues per side. Preheat oven to 450F. Lightly brush 4 tortillas with vegetable oil. Place tortillas, oil side down, on baking sheet. Combine grated cheeses in small bowl. Sprinkle 1/4 cup cheese mixture over each tortilla. Place chicken atop cheese, dividing equally. Place 1 onion slice and 1 egglpant slice atop each. Top each eggplant slice with 1 tortilla. Lightly brish tops of tortillas with oil. (Can be prepared 6 hours ahead. Cover and refrigerate.) Bake quesadillas until tortillas are slighlty crisp and cheese melts, about 10 mintues. Cut quesadillas into quarters. Serve with sour cream. Reprinted from Bon Appetits "Chefs at Home" magazine, Sept. 1997. Posted to MM-Recipes Digest V4 #224 by Julie Bertholf on Aug 25, 1997