In a bowl, combine olive oil, vinegar, garlic, and salt and pepper and blend until smooth.
Slice warm potatoes and place in another bowl. Pour oil–vinegar dressing over potatoes and toss gently. Sprinkle with parsley and red onions and toss again. Taste and add more salt and pepper, if desired. Add chicken and cooked beans to potatoes and mix gently. Garnish with cherry tomatoes.