Preheat your oven to 400°F (200°C) and prepare a large rimmed sheet pan by lining it with parchment paper for easy cleanup.
Dice the chicken breast into uniform 1-inch pieces to ensure they cook evenly alongside the vegetables.
Cut the broccoli into bite-sized florets and slice the zucchini into half-inch thick half-moons, measuring out a half cup.
In a small bowl, whisk together the lemon juice, lemon zest, water, dried oregano, garlic powder, sea salt, and black pepper to create a bright, oil-free marinade.
Place the chicken, broccoli, and zucchini in a large mixing bowl, pour the marinade over them, and toss with your hands or tongs until every surface is well-coated.
Spread the mixture onto the sheet pan in a single, even layer, making sure not to overcrowd the pan so the vegetables roast rather than steam.
Roast in the center of the oven for 18 to 20 minutes, or until the chicken is opaque and cooked through and the broccoli edges are slightly charred and crispy.
Serve immediately while hot, perhaps with an extra squeeze of fresh lemon if desired for an added pop of brightness.