Place eggs in a pot large enough to hold them with some space remaining. Fill pot with cold water to cover eggs by 1 inch. Cover and bring to a boil over high heat. Remove from heat and let eggs sit in hot water, off heat, for 25 minutes.
Fill a large bowl with half ice and half cold water. Transfer eggs to ice water and allow to cool for 10 minutes. Crack each egg and return to ice water. Remove shells.
Cut each egg in half lengthwise and remove yolks. Force yolks through a fine-mesh sieve into a large bowl. Add mayonnaise, mustard, curry powder and salt. Stir until blended and smooth.
Use a small spoon to fill each egg white with equal amounts of filling. (Alternatively, fill a pastry bag fitted with a star or plain tip and pipe filling into shells. Or use a ziplock bag with a small piece of a corner snipped off to pipe filling.) Garnish each egg with a small dollop of chutney.