Soak wooden skewers in water for at least 30 minutes if using.
In a large bowl, toss the 16 oz chicken breast cubes, 1 cup cherry tomatoes, 1 cup red onion, 1 cup yellow bell pepper, 1 cup zucchini, and 1 cup yellow squash with 2 tbsp olive oil, 1 tbsp lemon juice, 1 tsp kosher salt, and 0.5 tsp black pepper.
Thread the marinated chicken and vegetables alternately onto the soaked skewers, leaving a small space between items for even cooking.
Preheat the grill to medium-high heat. Place the loaded sticks on the grill.
Grill for 10 to 12 minutes, turning every 3 to 4 minutes, until the chicken reaches an internal temperature of 165°F and veggies are tender.
Remove from the grill, garnish with 2 tbsp fresh parsley, and serve immediately.