Place the chicken breasts in the bottom of the slow cooker. Add the minced garlic, lemon zest, lemon juice, cream of chicken soup, chicken broth, thyme, salt, and pepper.
Cover and cook on low for 4 hours.
Remove the chicken, shred it with two forks, and return it to the slow cooker. Stir in the uncooked rice.
Cover and cook on low for 1 more hour, or until the rice is tender.
Stir in the frozen peas and carrots. Cover and cook for 10 more minutes until the vegetables are heated through.
Sprinkle with fresh parsley before serving.