In a large resealable bag, combine 1/4 cup of the apricot preserves, the tamari, chili paste and sesame oil. Add the diced chicken and toss to combine. Marinate in the refrigerator for at least 4 hours or up to overnight.
Preheat a grill pan over medium heat. Thread each skewer in the following order: pepper, chicken, pineapple, chicken, pepper, chicken, pineapple. Repeat until all the chicken is used; reserve the marinade in the bag.
Drizzle the skewers with the olive oil and place them in the hot grill pan. Cook, rotating often, until the chicken is cooked through and edges of the pineapple are golden brown, about 10 minutes.
Meanwhile, place the reserved marinade and the remaining 2 tablespoons apricot preserves in a small saucepan and bring to a boil. Baste the skewers with this mixture 2 or 3 times during cooking.