Heat the oil in a large skillet over medium heat, then cook the chicken 5 minutes per side. Remove from pan.
Combine the remaining ingredients except apple juice and arrowroot powder in the pan and bring to a boil.
Return the chicken to the pan, reduce the heat to medium-low, and simmer 20 minutes or until the chicken has cooked through.
Whisk together the apple juice and arrowroot until a smooth slurry forms, then stir it into the pan and bring to a boil. Cook, stirring, until the sauce thickens, about 3 minutes.