Lightly sprinkle salt and pepper over chicken breasts. In a large heavy bottom pan, heat 1 tablespoon vegetable oil. Brown chicken breasts, approximately 3 minutes on each side. Transfer to slow cooker insert. Add cubed potatoes.
Add remaining 1 tablespoon vegetable oil to the pan. Fry onion, celery, and carrots for 2 minutes. Add minced garlic and thyme and continue to cook for 30 seconds.
Pour in 1 cup (240ml) water. Add Worcestershire sauce. When sauce comes to a boil, add salt to taste.
Turn off stove and pour contents over chicken and potatoes in slow cooker insert. Cover and cook on high for 4 hours.