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 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 evenly seasoning with the rosemary, thyme, oregano, salt, and pepper.
Simmer for about 5 to 10 minutes or until chicken is cooked through and sprouts are as tender as desired.
Remove from the heat, evenly sprinkle with pomegranate arils, and if desired add final drizzles of balsamic and/or honey, to taste. Serve immediately.
