Soak wooden skewers in water for 20 minutes to prevent burning during grilling.
Cut the chicken breast and halloumi cheese into uniform 1-inch cubes.
In a small bowl, whisk together the olive oil, lemon juice, dried oregano, garlic powder, sea salt, and black pepper to create the marinade.
Place the chicken, halloumi, zucchini rounds, bell pepper chunks, and onion wedges into a large bowl and pour the marinade over them, tossing to coat thoroughly.
Thread the marinated ingredients onto the skewers, alternating between the chicken, cheese, and various vegetables.
Preheat a grill or grill pan over medium-high heat and lightly grease the surface.
Grill the skewers for 10-12 minutes, turning every few minutes, until the chicken is cooked through and the halloumi has developed golden brown grill marks.