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Preheat oven to 425°F.
Toss broccoli and tomatoes in a large bowl with 2 tablespoons oil, ¼ teaspoon salt and pepper.
Cut chicken breasts into 4 equal portions. Brush the chicken with the remaining 1 tablespoon oil and sprinkle with lemon pepper seasoning and the remaining ¼ teaspoon salt. Place the chicken on one half of a rimmed baking sheet. Roast for 10 minutes. Remove from oven; carefully add the broccoli and tomatoes to the other side of the pan.
Continue roasting, stirring the vegetables once halfway through, until an instant-read thermometer inserted in the thickest part of a breast without touching bone registers 165°F and the vegetables are tender, 15 to 18 minutes more.
Sprinkle feta over the vegetables on the pan; stir to allow the feta to slightly melt. Serve the chicken and vegetables topped with the pan drippings.