Using a high-sided frying pan large enough to hold the chicken in a single layer, heat olive oil over medium-high heat. Place the chicken pieces in the hot pan, cover, and brown — about 5 minutes per side.
When browned, remove the chicken from the pan and set aside in the warm oven. Drain the pan of excess fat. Deglaze with vinegar. Add the garlic, shallot, and tomato. Cook briefly. Add the cream and stock. Return any chicken that is not cooked to the pan, lower heat, and simmer, covered, for 4 minutes.
Remove the chicken from the frying pan and set aside in the oven. Bring the sauce to a boil and reduce.
Divide chicken among warm serving dishes. Top with sauce. Sprinkle with parsley.