Place chicken, carrot, and onion in a 6-quart slow cooker. Pour marinara sauce over top and cook on high for 4 hours or on low for 6 hours or until chicken is cooked through and fork tender. When chicken is finished, shred with two forks.
Meanwhile, add chicken broth and milk to a large sauce pot and bring to a boil. Add in polenta and stir well. Lower heat to a low simmer and cook uncovered for 30 minutes stirring frequently. Add ¼ cup water if polenta becomes too thick.
Spoon polenta into bowls and top with chicken and sauce. Garnish with parsley and parmesan.
Notes
Polenta is a course ground yellow corn, just like grits. However, grits can also be made from ground white corn.
You can substitute any type of grits, but stone ground (not instant) has more flavor and add texture to the dish. Instant grits are too runny to hold up to the sauce in this dish.
The chicken would be equally as good served over pasta, I would use rigatoni or penne.
Chicken breasts can be substituted for the chicken thighs. I like chicken thighs because they have a bit more fat and come out moist not dry.