Bring mixture to a boil, constantly whisk until sauce is slightly thickened, about 1 minute.
Transfer 1 cup of the sauce to a bowl to use for basting the chicken.
Thread cut pieces of chicken on skewers. Season with salt and pepper on both sides.
Drizzle both sides of skewers with a small amount of oil to prevent sticking when cooking.
Preheat grill over medium-high heat. Clean grill and then use a paper towel dipped in oil to grease the grill.
Once the grill is hot add the skewers and cook for 4 minutes. Flip over and baste the cooked side with the sauce. Cook 4 minutes.
Repeat flipping, basting and covered cooking 2 additional times,
Sprinkle chicken yakitori skewers with sesame seeds (optional). Serve chicken skewers immediately with additional sauce.