Marinate the Chicken: In a bowl, season the chicken cubes with salt and pepper. Add a generous dollop of basil pesto and toss to coat evenly. Allowing the chicken to marinate for at least 30 minutes to let the flavors meld is a suggested option.
Assemble the Skewers: Preheat the grill to medium-high heat. Thread the marinated chicken, cherry tomatoes, bocconcini, and fresh basil leaves onto the skewers, alternating for a colorful and balanced presentation.
Grill to Perfection: Brush the skewers with olive oil to prevent sticking and a squeeze of fresh lemon juice to brighten the flavors. Grill the skewers for 8-10 minutes, turning occasionally, until the chicken is fully cooked and has a beautiful char. Ensure the tomatoes are softened, and the bocconcini has a slight melt.
Serve with a Drizzle: Arrange the skewers on a platter. Place the mozzarella balls randomly in and around the platter. Drizzle the remaining basil pesto over the skewers (making sure to cover the mozzarella balls) just before serving for an extra burst of flavor. Add fresh basil leaves and serve.