In a bowl, combine all the marinade ingredients.
Place the chicken cubes in the marinade, ensuring they are well coated. Cover and refrigerate for at least 30 minutes.
Preheat your grill to medium-high heat.
Thread the marinated chicken, red onions, red and yellow bell peppers, and courgettes onto the soaked wooden skewers, alternating the ingredients.
Drizzle the skewers with 2 tablespoons of olive oil and sprinkle with ground cumin, ground coriander, paprika, dried oregano, salt, and pepper.
Grill the chicken kebabs for about 12-15 minutes, turning occasionally, until the chicken is cooked through and the vegetables are tender and slightly charred.
Serve the chicken kebabs hot with your choice of side dishes.