Place the olive oil, vinegar, mustard, salt and pepper in a bowl and whisk to combine.
Soak 6 wooden skewers in cold water for at least 30 minutes or use metal skewers.
Thread the chicken, bratwurst, and vegetables onto the skewers and place on a sheet pan. Brush the skewers generously with the marinade and refrigerate for 15 minutes.
Preheat grill to medium high heat. Cook skewers for 5-7 minutes on each side or until chicken and bratwurst are cooked through. Makes at least 4 skewers.