Soak wooden skewers in water for at least 20 minutes to prevent them from burning on the grill.
Cut the chicken breast, halloumi cheese, zucchini, and red bell pepper into uniform 1-inch cubes; cut the red onion into similar-sized wedges.
In a small mixing bowl, whisk together the extra virgin olive oil, lemon juice, dried oregano, garlic powder, sea salt, and black pepper to create the marinade.
Thread the chicken, halloumi, zucchini, bell pepper, and onion onto the skewers, alternating the ingredients for even cooking and flavor distribution.
Brush the prepared marinade generously over all sides of the skewers using a pastry brush.
Preheat a grill or a cast-iron grill pan over medium-high heat until it is very hot.
Place the skewers on the grill and cook for 10-12 minutes, rotating every few minutes, until the chicken is fully cooked and the halloumi has developed deep golden-brown grill marks.
Remove from heat and let rest for 2 minutes before serving.