Season chicken with salt and pepper on both sides.
Mix sour cream with relish and ketchup, and spread some on each cutlet. Divide the sauerkraut, cheese and meat between 4 cutlets and top with remaining 4 cutlets, dressing side down. Press edges to seal.
Set up 3 dishes on the counter; one with the flour, one with the beaten egg and one with both breadcrumbs. Dredge the stuffed cutlets first in the flour, then the egg and finally in the breadcrumb mix.
Heat a shallow layer of oil in large skillet over medium to medium-high heat. Cook chicken Reubens 3-4 minutes on each side until deeply golden and cooked through. Let drain on a cooling rack for a minute. Garnish with chopped dill or parsley and serve with lemon wedges and a pickle alongside.