Preheat the oven to 400°. On a large rimmed baking sheet, season the chicken with salt and pepper. Roast on the top shelf of the oven for 25 minutes, until the skin is golden and crisp and the meat is cooked through. Transfer the chicken to a platter. Increase the oven temperature to 450°.
Meanwhile, in a medium skillet, heat the oil. Add the onion and cook over moderately high heat until softened, about 3 minutes. Add the beef, garlic, cumin and paprika and cook, breaking up the meat with a wooden spoon, until no pink remains, about 5 minutes. Season with salt and pepper.
In a food processor, puree the corn with the basil. Scrape the puree into a large saucepan and cook over high heat, stirring, until thickened, about 4 minutes. Season the puree with salt.
Spread the ground beef mixture in four 12-ounce gratin dishes. Set the chicken and eggs on the meat and sprinkle with the olives and raisins. Spread a 1-inch-thick layer of the corn puree on top of each dish. Bake the gratins on the top shelf of the oven for 10 minutes, until bubbling and heated through. Serve hot.