Cut the red and green bell peppers and the red onion into 1-inch pieces; set aside.
Trim and cut the chicken breasts into 1-inch pieces and place them in a large bowl or a gallon-sized resealable bag.
In a small bowl, combine the oregano, cumin, garlic powder, cayenne pepper, black pepper, and salt; mix until evenly blended.
Add the olive oil and lime juice to the seasoning, stir to combine, then pour the marinade over the chicken in the bowl or bag and toss to coat.
Marinate the chicken in the refrigerator for at least 1 hour.
When ready to cook, thread the chicken pieces and vegetables onto skewers, alternating chicken with peppers and onion and leaving about 2 inches of skewer exposed for handling.
Preheat the grill to medium (or preheat the oven to 350°F if baking). Lightly brush vegetables with oil if desired.
Grill the kabobs over indirect/medium heat for 10–15 minutes, turning once halfway through, until chicken is cooked through and reaches 165°F on an instant-read thermometer.
Remove kabobs from the grill and serve immediately.