Place chicken in a 3 1/2- to 4-quart slow cooker. Add the next five ingredients (through salt).
Cover and cook on low for 7 to 8 hours, or on high for 3 1/2 to 4 hours.
If using low, turn cooker to high. In a small bowl, whisk together the half-and-half and flour; add to soup in cooker. Stir in peas, goat cheese (if using), and thyme. Cover and cook 15 minutes more, or until thickened.