Grease a 4- to 6-quart slow cooker with the olive oil.
Place onion, chicken breasts, mushrooms, and garlic into the slow cooker. Pour in the marsala wine. Sprinkle the sea salt and black pepper over the chicken.
Cover and cook on LOW for 4 hours.
Remove the chicken from the slow cooker and set aside.
Add heavy cream and xanthan gum to the sauce in the slow cooker and stir to combine. Return the chicken breasts to the slow cooker. Cover and cook on HIGH for 30 minutes.