Whisk together the olive oil, lemon juice, garlic, cumin, paprika, salt, and pepper in a large bowl.
Add the chicken to the marinade and toss to coat. Cover and refrigerate for at least 30 minutes, up to 12 hours.
If using wooden skewers, soak them in water for 30 minutes before assembling.
Preheat the oven to 400°F. Line a baking sheet with foil or parchment.
Thread the chicken, bell pepper, and onion onto the skewers, alternating pieces.
Arrange the skewers on the baking sheet in a single layer, spaced at least an inch apart.
Bake for 18 to 22 minutes, flipping once halfway through, until the internal temperature reaches 165°F.
For light charring, broil for 1 to 2 minutes at the end, watching closely.
Let the kabobs rest for 5 minutes before serving.