This recipe started from a recreational class at the Institute of Culinary Education in NYC, with some added ingredients inspired by the tuna tartare at Bobby Flay's restaurant. Cook time is refrigeration/marinating time.
Gently comibine all ingredients, except for the cucumbers and chives, in a large bowl. Cover with plastic wrap and refrigerate for about 2 hours.
To serve as hand-held hors d'oeuvres, cut the cucumber into 3/4" slices and use a melon baller to scoop out a hollow in the center of each slice (be careful not to scoop all the way through). Spoon the marinated tuna into the cucumber "cups". Garnish with chives.
Alternately, cut the cucumber into 1/4" slices and serve as "chips" for the tartare.