Preheat your grill to medium-high. Brush the chicken with the olive oil; season with the cumin, chili powder, salt and pepper. Grill for 3-4 minutes per side, or until cooked through. Cool the chicken to room temperature, then cut into small cubes and place in a bowl. Mix in the remaining ingredients, except the avocados. Cover and chill for at least 30 minutes. Cut the avocados lengthwise in half and carefully remove the pit. Trim a little from the bottom of each half so they will sit straight and divide among 4 plates. Divide and mound the chicken mixture on the avocados and then serve.
Recipe Options: Use an equal weight of boneless chicken thigh instead breast. Use light mayonnaise instead of regular. Give the salad a spicier bite by mixing in 1 tablespoon or so of finely chopped jalapeño pepper. Stuff the chicken salad into papaya halves (seeds removed), instead of avocadoes.