Put the chicken in another bowl and add 1/4 cup of the sauce. Prepare a gas or charcoal grill for medium-hot direct grilling, or place a heavy, lightly oiled skillet over medium-high heat on the stovetop.
Cook the chicken about 5 minutes per side, turning frequently, until the chicken is cooked through. Transfer to a cutting board and let it rest for 10 minutes before slicing 1/2-thick.
Serve the chicken sprinkled with the green onion and additional sauce drizzled over.