Place zest, orange juice, lemon juice, and soy sauce in a large nonreactive bowl and whisk until combined. Add chicken and toss to coat. Cover and refrigerate for 30 minutes.
For the skewers:
Heat a grill pan or a gas or charcoal grill to medium (about 350°F). Rub the grill with a towel dipped in oil.
Remove chicken from marinade. Alternately thread 5 pieces of pepper and 4 pieces of chicken onto each skewer, beginning and ending with peppers, and leaving 1/4 inch between each piece. Season all over with salt.
Place on the grill and cook, covered and turning often, until chicken is opaque, firm, and cooked through and peppers are charred, about 30 to 40 minutes. Serve immediately with dipping sauce.