Place eggs in a saucepan; cover with water. Bring to a boil, remove from heat, and let eggs stand in hot water for 15 minutes.
Remove eggs from hot water, cool under cold running water, and peel.
Cut each egg in half lengthwise; place egg yolks in a bowl. Mash yolks with a fork; stir in 3 tablespoons goat cheese, 2 tablespoons pecans, mayonnaise, chutney, salt, and pepper.
Place egg white halves cut-side-up on a serving platter. Spoon yolk mixture into whites, cover, and refrigerate until ready to serve. Immediately before serving, sprinkle with remaining goat cheese and pecans.
