Bring water to a boil, add garlic and chicken breast. Reduce to a simmer, cover and cook for 15 minutes or until chicken is cooked through, turning chicken over halfway during cooking.
Remove chicken and garlic from stock and set aside. When chicken is cool enough to handle, cut into small cubes.
Blanch beans in the leftover stock for three to four minutes or until tender but still crisp. With a slotted spoon transfer beans to a large bowl. Add potatoes to the boiling stock, reduce to a gentle boil and cook for 15 minutes or until tender. Drain and peel the potatoes. Reserve the stock. Cut potatoes into large chunks and add to the beans.
In a food processor, combine reserved garlic and add four to five tablespoons stock, basil, mayonnaise, lemon zest, lemon juice and salt. Puree until smooth. Pour the dressing over the chicken mixture. Toss well to coat. Serve on a bed of salad greens.