In a small saucepan, stir together the mirin, sake, soy sauce and sugar. Bring the mixture to a boil over medium-high heat, then pull the pan off the burner. Set aside half of this sauce for dipping; the rest will be used to baste the chicken.
Thread the peppers evenly onto 2 metal or soaked wooden skewers. Thread the chicken pieces separately onto 6 metal or soaked wooden skewers. Heat the grill to medium, and have the basting sauce and a brush ready next to the grill.
Arrange the chicken skewers on the grill grates, and grill, covered, until the meat is cooked through, 10 to 12 minutes, turning the chicken skewers while they cook and basting frequently, especially during the final three minutes of cook time. Grill the peppers, covered, until they're tender, four to five minutes, giving them an occasional turn. At the end, grill the green onions for one to two minutes, until they're slightly charred and tender. Serve the chicken and vegetables with the reserved sauce for dipping.
