In a bowl with lid or in a sealable bag, mix together balsamic vinegar, 1/4 cup olive oil, salt, and pepper. Once mixed, add chicken. Cover bowl or seal bag and shake to ensure that all chicken is coated with marinade. Place in refrigerator for at least 2 hours.
When ready to cook, remove chicken from marinade. Mix together herbs de Provence and salt. Coat skin side of chicken with the spice mixture.
Heat 1 tbsp olive oil in Instant Pot on saute mode. Add 4 pieces of chicken, skin side down, and cook for 5 minutes. Remove from pot and add the other 4 pieces of chicken skin side down. Again, cook for 5 minutes and then remove chicken from pot.
Add white cooking wine to pot to deglaze bottom of the pot. Once the pot has been deglazed, add chicken broth.
Place Instant Pot steaming rack in pot. Stack chicken on rack, placing the legs and thighs on the bottom, and the breasts and wings on top.
Seal pot and cook on high pressure for 10 minutes. Let natural release for 10 minutes. Remove chicken from pot and serve warm.