1. In a large bowl, whisk together 1/4 cup olive oil, lemon juice, minced garlic, oregano, thyme, paprika, salt, and pepper. Add the chicken cubes and toss to coat. Cover and marinate in the refrigerator for at least 30 minutes (or up to 4 hours).
2. While the chicken marinates, prepare the vegetables. Cut zucchini into 1-inch rounds or half-moons. Chop bell peppers into 1.5-inch chunks. Cut red onion into 1.5-inch wedges, separating the layers. Keep cherry tomatoes whole.
3. If using wooden skewers, soak them in water for at least 30 minutes to prevent burning.
4. Preheat your grill to medium-high heat.
5. Thread the marinated chicken and prepared vegetables (zucchini, bell peppers, red onion) onto the skewers, alternating ingredients. You can add cherry tomatoes now or reserve them to add during the last few minutes of grilling.
6. Brush the grill grates lightly with olive oil.
7. Place the kabobs on the preheated grill. Grill for 15-20 minutes, turning occasionally, until the chicken is cooked through and the vegetables are tender and slightly charred.
8. Brush the kabobs with the remaining 1/4 cup of olive oil during the last few minutes of cooking if desired, for extra shine and flavor.
9. Remove from grill and let rest for a few minutes before serving.