Cut the chicken breast into 2 inch pieces. Combine the chicken with 1/2 cup mayonnaise, 3 grated garlic cloves, 1 tbsp grated onion, 2 tbsp white wine, 1 tsp salt, and 1/2 tsp black pepper. Cover and refrigerate overnight.
Cut the bell pepper and red onion into large chunks. Toss the bell pepper and onion with 1/2 tsp salt, 1/2 tsp black pepper, and 3 tbsp olive oil.
Place the marinated chicken and chopped vegetables on skewers. Grill on high heat for about 15 minutes, turning one half way through. Grilling time may vary depending on the size of your chicken and type of grill.