Preheat your oven to 400°F and line a large baking sheet with parchment paper.
Chop the broccoli, red bell pepper, and zucchini into bite-sized pieces and place them on the baking sheet.
Drizzle the vegetables with olive oil, sprinkle with sea salt and black pepper, and toss to coat evenly.
Roast the vegetables for 20-25 minutes until they are tender and slightly charred at the edges.
While vegetables roast, place the chicken breast in a small pot and cover with water; bring to a gentle simmer.
Poach the chicken for 12-15 minutes until fully cooked through, then remove from the liquid and let rest for 5 minutes.
Use two forks to shred the chicken into thin strips and place in a mixing bowl.
Whisk together the lemon juice, minced garlic, and dried oregano, then toss the shredded chicken in this mixture.
Serve the zesty shredded chicken over the bed of roasted rainbow vegetables.