1. Place chicken in a saucepan; add water to cover. Bring to a boil; reduce heat, and simmer 18 minutes or until chicken is done. Remove from pan; let cool. Place chicken in a food processor. Pulse 3 to 5 times or until chicken is finely chopped.
2. Combine chicken, mayonnaise, and next 6 ingredients in a bowl; stir until combined. Spoon about 1 tablespoon chicken mixture into each phyllo shell. Serve immediately, or cover and chill up to 2 hours. Garnish with fresh dill sprigs, if desired.