To a large skillet, add the olive oil, chicken, and cook over medium-high heat for about 5 minutes, or until chicken is about 80% cooked through; stir and flip intermittently to ensure even cooking.
Push chicken over to one side of the skillet and add the Brussels sprouts in an even, flat layer with the cut side down. Allow them to cook for about 2 minutes before evenly drizzling the entire skillet with balsamic vinegar, honey, and seasoning with the rosemary, thyme, oregano, salt, and pepper.
Simmer for about 5 to 10 minutes or until chicken is cooked through and Brussels sprouts are as tender as desired.
Remove from heat, sprinkle with pomegranate arils, and add final drizzles of balsamic and/or honey, to taste. Serve immediately.
