Preheat the oven to 350°F (175°C) and lightly grease a 13 x 9 x 2-inch baking dish with nonstick spray.
Season both sides of the chicken breasts with salt and pepper; set aside.
Place the melted butter in one shallow dish.
In a second shallow dish, combine the Italian bread crumbs, grated Parmesan, and garlic powder.
Dip each chicken breast into the melted butter, then press into the parmesan-breadcrumb mixture to coat evenly; arrange the coated chicken in the prepared baking dish.
In a medium bowl, toss the sliced zucchini, sliced yellow squash, and quartered baby red potatoes with the olive oil until evenly coated.
Arrange the vegetables around the chicken in the baking dish in a single layer as much as possible.
Bake for 30–40 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the vegetables are tender; timing depends on chicken thickness and potato size.
Remove from the oven and let rest 5 minutes before serving.