Add the oil to a 12-inch non-stick high-sided skillet (AKA a chicken fryer).
Place over medium-high heat for 2 minutes.
Add the brussels sprouts and sweet potatoes.
Cook for 8 minutes, stirring occasionally.
Add the chicken, onion, salt, pepper, and rosemary to the skillet.
Cook for 6 minutes, carefully stirring occasionally (skillet will be full).
Reduce the heat to medium-low.
Add the pomegranate juice, honey, and balsamic vinegar to the skillet.
Let the liquid simmer for 5-10 minutes, stirring occasionally, until most of the liquid has been evaporated/absorbed and the remaining liquid has thickened.
Remove the skillet from the heat. Top with pomegranate arils.