Pat the chicken dry with paper towels. Season the skin with the salt, pepper, and thyme.
Fill the cavity with lemon halves and two cloves of garlic.
Arrange the carrots, potatoes, and onion in the bottom of the slow cooker.
Place the chicken on the vegetables and scatter the rest of the garlic.
Add chicken broth to the cooker. Squeeze any remaining lemon over the chicken.
Cook for 6 to 7 hours on LOW or 3 to 4 hours on HIGH, until a food thermometer reads at least 165°F (74°C) in the innermost thigh and wing and the thickest part of the breast, without touching bone.