Begin by cutting the chicken breasts into 1-inch cubes and placing them in a large mixing bowl.
In a separate bowl, whisk together the olive oil, lemon juice, minced garlic, ground cumin, paprika, dried oregano, salt, and pepper to create the marinade.
Pour the marinade over the chicken and toss well to ensure all pieces are coated. Cover and refrigerate for at least 20 minutes (or up to overnight for more flavor).
If using wooden skewers, soak them in water for about 30 minutes to prevent burning.
Preheat the grill or grill pan over medium-high heat.
Thread the marinated chicken cubes onto skewers, alternating with pieces of bell pepper, onion, and zucchini.
Place the skewers on the grill and cook for 12-15 minutes, turning occasionally, until the chicken is cooked through and has nice grill marks.
Remove the kabobs from the grill and let them rest for a few minutes before serving.