Rinse chicken, pat dry, and cut into 1/2-inch chunks.
In a 12-inch nonstick frying pan or a 5- to 6-quart nonstick pan over high heat, stir chicken in oil until lightly browned and no longer pink in center of thickest part (cut to test), 4 to 5 minutes.
Add blood orange sauce and stir until boiling, 1 to 2 minutes.
Spoon chicken and sauce onto rice. Sprinkle with green onions and season to taste with soy sauce.