In a large bowl, whisk together the olive oil, lemon juice, minced garlic, oregano, salt, and black pepper to make the marinade.
Add the chicken cubes to the bowl and toss until evenly coated. Let the chicken marinate for 15 minutes while you prepare the vegetables.
Thread the chicken, zucchini rounds, bell pepper pieces, red onion pieces, and cherry tomatoes onto skewers, alternating the items for even cooking.
Heat a grill to medium-high heat. Place the skewers on the grates and cook for 10 to 12 minutes, turning every 3 minutes, until the chicken reaches 165°F and the vegetables are lightly charred.
Remove the skewers from the grill and sprinkle with chopped fresh parsley before serving.