Place egg in a saucepan and cover with cold water. Bring water to a boil and immediately remove from heat. Cover and let eggs stand in hot water for 10 to 12 minutes.
Remove from hot water, cool, peel, and chop.
Before cooking the beets, wash them gently under cold water, being careful not to pierce the thin skin.
Place in a saucepan and cover with cold water. Bring water to a boil and cook until they pierce easily with a thin knife, about 15 minutes.
To peel cooked beets, cut off both ends, then hold the beets under cold running water and slip off the skins. Leave to cool until able to handle, then grate them into a medium bowl.
Add eggs, mayonnaise, salt and pepper; mix gently. Cover and chill for at least 1 hour before serving.
