Place chicken in a dish with 1½ cups teriyaki sauce. Cover and refrigerate for 8 hours or overnight.
Preheat grill to high heat. Lightly oil the grates.
Remove chicken from marinade and discard the used marinade.
Grill chicken 8 minutes per side or until fully cooked.
Brush remaining ½ cup teriyaki sauce on chicken during last 5 minutes of grilling.
Top each piece with a pineapple ring and brush with melted butter. Grill 1–2 more minutes.
In a saucepan, mix brown sugar, soy sauce, pineapple juice, and Worcestershire sauce. Simmer until sugar dissolves.
Serve chicken topped with pineapple and drizzle glaze over or serve on the side.
