Cut tuna into 1/4-inch dice, and roughly chop until tuna holds together.
In a medium bowl, combine tuna, sesame oil, soy sauce, vinegar, and chives. Season with salt and pepper. Cover, and refrigerate until serving, up to 1 hour.
When ready to serve, slice radishes with a mandoline. Using a 1-inch cookie cutter as a mold, press 1 heaping teaspoon of tartare mixture onto a radish disk, forming a cylinder. Garnish each with 2-inch pieces of chives. Repeat with remaining tartare and radishes.
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