In medium saucepan, cover eggs with 2 inches of water. Heat to boiling over high heat. Cook 1 minute. Reduce heat to medium and cook 5 minutes. Add green beans and cook 5 to 7 minutes longer, or until beans are tender and eggs are hard-boiled. Drain and rinse under cold water. Transfer eggs and green beans to a bowl of ice water to cool quickly. Drain when cooled completely. Shell and quarter eggs.
In small bowl, combine vinegar, shallot, mustard, sugar, salt, and pepper. Slowly whisk in oil until dressing thickens slightly and is well combined.
In large bowl, combine salad greens and half of dressing; toss to coat. Add chicken, green beans, olives, radishes, and egg quarters. Drizzle with remaining salad dressing and serve.
