Pre-heat an outdoor or indoor grill to medium-high heat.
Pre-heat the broiler.
To make the sauce, heat EVOO in a skillet over medium-high heat. Add the onions and garlic, and cook until softened, about 5 minutes. Add the tomatoes and let simmer for another 5 minutes.
Drizzle the eggplant slices and chicken cutlets with EVOO and season with salt and pepper. On one half of the grill place the eggplant slices. On the other half, place the chicken cutlets. Cook the eggplant and chicken for about 4 minutes per side. There should be no pink in the middle of the chicken.