Cut the chicken breast into 1-inch cubes and place them in a medium glass bowl.
In a small jar, whisk together the olive oil, lemon juice, minced garlic, dried oregano, sea salt, and black pepper.
Pour the marinade over the chicken cubes, tossing well to coat, and let marinate in the refrigerator for at least 30 minutes.
Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Thread the marinated chicken, red bell pepper chunks, and red onion pieces onto wooden or metal skewers, alternating ingredients.
Place the skewers on the prepared baking sheet and roast for 18-20 minutes, turning halfway through, until the chicken is golden brown and cooked to an internal temperature of 165°F.
While the skewers roast, stir the chopped fresh dill into the Greek yogurt to create a cooling dipping sauce.
Serve the warm skewers immediately with the dill yogurt sauce on the side.