Mix the chicken, breadcrumbs, Parmesan, egg, milk, garlic, basil, salt and pepper just until combined.
Shape the mixture into 20 meatballs and arrange them on a parchment-lined sheet pan.
Broil until the tops are lightly browned and the meatballs hold their shape, 5 to 6 minutes; they will not be cooked through.
Stir the tomatoes and oregano in a 6-quart slow cooker and nestle the meatballs into the sauce.
Cover and cook on low until the centers reach 165°F, 3 1/2 to 4 hours.
Scatter the mozzarella over the meatballs, cover and cook on high until melted, 10 minutes.
Spoon the meatballs and thick tomato sauce into shallow bowls.