Cut the eggs in half and take out the yolks. Combine the yolks with the mustard, yogurt and olives, add some pepper and puree until smooth. Spoon the mixture into the egg halves (about 1 tablespoon for every egg half).
Dot small amounts of the mayonnaise (about half a teaspoon) around a large plate and place the eggs on top to prevent them from slipping. Garnish with the radish (cut into thin sticks) and chives, season, drizzle with a little olive oil and serve.