Preheat oven to 375 degrees. Spray a 13 x 10 inch aluminum foil pan with vegetable oil cooking spray.
Slice eggplant lengthwise. Melt butter in a large heavy skillet and cook onion over low heat until very soft, about 5 minutes. Add garlic and cook about a minute more. Add chicken and cook for about 6 minutes. Add alfredo sauce, cheese, salt and pepper. Cook for 3 to 4 minutes and turn off heat.
Spoon about 2 Tbsp of sauce into prepared pan. Cover bottom of pan with eggplant slices. Spoon 1/3 of sauce over eggplant, distributing half of chicken evenly. Layer more eggplant, 1/3 of sauce and remaining chicken. Cover with eggplant and remaining sauce. (Do not use any chicken on top layer...just sauce). Make sure all edges of eggplant are coated with sauce. Top with parmesan. Bake for 20-25 minutes, uncovered until bubbly. Allow to sit for 10 minutes before slicing.