Adobo seasoning is a handy all-purpose seasoning blend featuring onion, garlic, black pepper, and other spices. Look for it with the dried spice and herb blends.
Preheat the oven to 375°F. Massage oil onto each piece of chicken. Season chicken on both sides with salt and black pepper, then sprinkle with 2 tablespoons of the adobo seasoning. Arrange chicken in a single layer in a baking dish.
Stir together tomatoes, onion, bell pepper, garlic and the remaining tablespoon of adobo seasoning in a large bowl. Pour tomato mixture over the chicken. Cover the baking dish with foil and bake until chicken is cooked through, about 35 minutes.
Remove chicken from the baking dish. Shred each breast with a fork, return it to the baking dish and gently stir to mix the chicken with the cooked vegetables. Serve by spooning the mixture over cooked rice or in tortillas.