Place the chicken breasts in the bottom of the slow cooker.
Add the sliced mushrooms, diced onion, and minced garlic on top of the chicken.
Sprinkle the dried thyme, salt, and black pepper over the ingredients.
In a bowl, stir together the chicken broth and cream of mushroom soup until smooth, then pour the mixture over everything in the slow cooker.
Cover and cook on low for 4 hours.
Stir in the uncooked rice, making sure it sits in the liquid. Cover and cook for 1 more hour, or until the rice is tender and the chicken reaches 165°F.
Remove the chicken, shred or slice it, then return it to the slow cooker. Stir in the heavy cream until the sauce turns creamy and everything is well combined.