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.
Nutrition Information for 1 Serving (1/6th of Entire Recipe): Calories 370, Total Fat 12.5 g, Total Carbohydrate 23.8 g, Dietary Fiber 4.7 g, Sugars 17.2 g, Protein 44.0 g