In a small bowl, combine 1 teaspoon salt, 1/4 teaspoon ground black pepper, and 1/4 teaspoon ground cayenne pepper.
Rub the spice mixture evenly onto the 4 skinless boneless chicken breast halves.
Heat 2 tablespoons of olive oil in a skillet over medium heat.
Cook the chicken in the heated oil until no longer pink in the center and the juices run clear, about 5 to 7 minutes per side.
In a separate bowl, mix together 1 minced red onion, 2 tablespoons lime juice, and 1 diced avocado.
Season the avocado mixture with ground salt and black pepper to taste.
Spoon the avocado mixture over the cooked chicken breasts to serve.