In a large bowl, whisk together vinegar, 2 tablespoons olive oil, the cumin, salt, and pepper. Add avocado, papaya, sweet pepper, and cilantro; toss together. Set aside.
Lightly sprinkle both sides of the chicken with blackened steak seasoning.
In a large ovenproof skillet, brown the chicken on both sides in the 1 tablespoon hot olive oil, turning once. Bake in a 375 degree F oven for about 15 minutes or until the chicken no longer is pink. Don't turn. (Or omit the browning and place the chicken in an 8x8x2-inch [2-quart square] baking dish brushed with olive oil. Bake in 375 degree F oven 15 to 20 minutes or till the chicken no longer is pink.)
To serve, spoon some of the salsa over the chicken. Pass the remaining salsa or serve it with chips, if you like.
