Spray a 6 quart Slow Cooker lightly with non-stick spray. Add the squash, peppers, onion, garlic, hominy, chilies, and black beans to the cooker and stir to combine.
Combine the pureed beans, chicken stock, and red chili sauce in a bowl. Add the masa harina and stir or whisk until the mixture is smooth.
Add the chili powder, cumin, and oregano to the liquid ingredients and stir once more. Pour the liquids into the cooker and stir to combine everything well.
Cut the chicken into bite size pieces. Lay the chicken pieces on top of the vegetable mixture. Cover and cook on Low for 6 - 8 hours (the heat on every slow cooker is different so adjust the time according to how yours cooks).
At the 6/8 hour point, stir the chicken into the other ingredients. Give things a taste and add more of any seasoning you think it needs.
Tilt the lid slightly and turn the heat setting to High. Allow the chili to cook until it is the thickness that you like.
While the chili is cooking on High, mix the sour cream, salsa, and cilantro together. Set aside.
When you are ready to serve, ladle into bowls. Pass the sour cream mixture, lime, and cheese at the table.