Remove and discard skin and any excess fat from chicken. Moderately sprinkle both sides of each chicken piece with salt, pepper, and paprika. Heat olive oil in a large non-stick skillet and add half the chicken pieces and cook, turning pieces until golden brown, for 4 to 6 minutes. Remove to a plate and repeat with remaining chicken.
Reduce heat to medium-low and add onion and garlic. Cook, stirring, for 1 minute. Stir in tomatoes, vinegar, Italian seasoning, and basil. Bring mixture to a boil.
Nestle chicken pieces into tomato mixture in the pan, reduce heat and simmer uncovered, turning chicken occasionally. Cook for about 20-30 minutes. Chicken is fully cooked when juices run clear.
Stir in artichokes and zucchini, cover and simmer for 5 minutes or until zucchini is barely tender.
Stir in parsley and olives, and serve over your pasta of choice.