Soak bamboo skewers in a shallow tray for about 15 minutes.
Put the bread in a food processor and process to crumbs. Transfer to a bowl, stir in the cheese and season.
Put the chicken into a bowl and use 4 tbsp of mayonnaise mixture to coat the chicken pieces. Save the remainder of the sauce for dipping.
Weave the chicken onto bamboo sticks and toss into the bread crumb and cheese mixture. Place onto a non-stick baking sheet and drizzle with oil.
Cook under a preheated hot grill for 4-5 minutes on each side. Serve with the remaining mayonnaise and lemon wedges.