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 1-inch pieces suitable for skewering.
In a small bowl, whisk together the olive oil, lemon juice, dried oregano, garlic powder, sea salt, and black pepper to create the marinade.
Pour the marinade over the chicken and vegetables, tossing well to ensure every piece is evenly coated.
Thread the marinated chicken and vegetables onto wooden or metal skewers, alternating between protein and produce.
Preheat a grill or grill pan over medium-high heat and lightly grease with a touch of oil if necessary.
Grill the skewers for 10-12 minutes, turning occasionally, until the chicken is cooked through and the vegetables have developed a light char.
While the skewers cook, stir the fresh dill into the Greek yogurt to create a high-protein dipping sauce.
Remove the skewers from the heat and serve immediately with the chilled yogurt dip on the side.