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