Prepare kabobs. Whisk together avocado oil, sea salt, black pepper, dried oregano, and lime juice in a large bowl. Add in chopped chicken, bell peppers, and red onion and toss to coat in marinade. Cover and refrigerate for 30-60 minutes to marinate.
Heat grill to medium heat.
Using metal skewers, layer marinated chicken with onions and bell peppers. Repeat until remainder of vegetables and chicken are used.
Grill kabobs for 10 minutes, flip, and grill an additional 8-10 minutes, or until chicken is golden and cooked through.
While kabobs are on the grill, prepare avocado sauce. Add all ingredients to a food processor and pulse on high until mixture is smooth and creamy.
Remove kabobs from grill and carefully remove skewers. Dollop avocado sauce on top and devour!