Place pomegranate juice and cornstarch in a small bowl, stir until mixture is combined. Reserved.
CHICKEN: Heat oil on medium-high in a large deep skillet. Brown chicken, about 2 minutes per side. Remove from skillet. Reserve.
Add carrots and sliced onion to skillet. Cook on medium heat 5 minutes, stirring often. Add reserved glaze mixture. Bring to a boil, lower heat to medium-low and simmer for 5 minutes. Add back browned chicken. Cook for an additional 5 minutes, turning occasionally to coat with glaze.
Remove chicken and place on clean dish. Add reserved cornstarch mixture into skillet; stir to combine well.
Bring glaze to boil and allow to thicken. Add pomegranate seeds and place chicken back in skillet and turn to coat with glaze. Serve on rice.