Heat the olive oil in a large stock pot set over medium heat. Add the onion and garlic and cook, stirring occasionally, until softened and beginning to turn a golden, about 7 minutes. Lower the heat if they begin to burn at any point. Add the crushed tomatoes and the tomato paste and stir until the mixture is smooth and well-combined. Add the oregano, sugar, salt, and pepper; stir, and bring the mixture to a simmer.

Pour 2 cups of the sauce in the base of a 6-quart slow cooker. Add the chicken breasts and pour the remaining sauce evenly over the top. Cook on low for 8 hours.

To serve, divide the chicken breasts among 6 serving plates, spoon 2 tablespoons of the marinara sauce over the top, and sprinkle each evenly with the basil and Parmesan cheese.