In a mixing bowl, combine olive oil, lemon juice, minced garlic, paprika, cumin, salt, and pepper. Whisk until well mixed.
Cut the chicken breasts into 1-inch cubes and add them to the marinade. Stir to coat the chicken evenly. Cover and refrigerate for at least 15 minutes, or up to 2 hours for more flavor.
Preheat the grill or grill pan over medium-high heat.
While the grill is heating, prepare the vegetables. Thread the marinated chicken, bell pepper pieces, red onion wedges, zucchini slices, and cherry tomatoes onto the skewers, alternating between chicken and vegetables.
Once the grill is ready, place the skewers on the grill and cook for 12-15 minutes, turning occasionally, until the chicken is cooked through and reaches an internal temperature of 165°F (75°C).
Remove the kabobs from the grill and let them rest for a few minutes before serving.
Serve with rice, pita bread, or a fresh salad for a complete meal.