Cut the chicken breast into 1-inch cubes and place them in a medium mixing bowl.
Chop the red bell pepper, zucchini, and red onion into bite-sized pieces roughly the same size as the chicken cubes.
In a small bowl or jar, whisk together the extra virgin olive oil, lemon juice, minced garlic, dried oregano, sea salt, and black pepper.
Pour the marinade over the chicken and vegetables, tossing thoroughly to ensure every piece is well-coated, and let it marinate for 10 to 15 minutes.
If using wooden skewers, soak them in water for 20 minutes; otherwise, thread the chicken and vegetables onto metal skewers, alternating between protein and produce.
Preheat a grill pan or outdoor grill to medium-high heat and lightly brush with a high-smoke point oil if necessary.
Grill the skewers for 10-12 minutes, turning every few minutes, until the chicken is golden brown and cooked through and the vegetables have developed a slight char.