Put potatoes and onion in a 6-quart slow cooker. Add broth, garlic, oregano, 1 teaspoon salt, and black pepper.
Cover; cook on low 1 1/2 hours to start potatoes.
Season chicken with remaining salt; arrange over vegetables in one layer.
Cover; cook on low 2 1/2 to 3 hours until thickest breast reaches 165°F and potatoes are tender.
Transfer chicken and vegetables to a platter; switch cooker to high.
Stir in lemon zest and juice. Whisk cornstarch and water; add to liquid.
Cook uncovered 5 to 8 minutes until lightly thickened. Spoon sauce over sliced chicken.