Combine first 5 ingredients; stir in 1/2 teaspoon oil. Place shallot mixture in a large zip-top plastic bag; add chicken to bag. Seal and marinate in refrigerator 3 hours to overnight, turning bag occasionally.
Combine ketchup and next 4 ingredients (through vinegar).
Heat remaining 1 teaspoon oil in a large nonstick skillet over medium-high heat. Remove chicken from bag; discard marinade. Add chicken to pan; cook 2 minutes on each side or until browned. Cover, reduce heat to medium-low, and cook 8 minutes or until done, turning twice. Serve with ketchup mixture.