Using a mandolin, shave the fennel into paper-thin slices. Submerge the fennel in a bowl of cold water. Cover and refrigerate for about 1 hour, or until cold and crisp. Drain well.
In a large bowl, combine the fennel, parsley, and chives. Using a microplane grater, grate the lemon zest over the fennel mixture. Into a small bowl, squeeze the lemon juice. Slowly drizzle the olive oil into the lemon juice while whisking. Season to taste with salt and pepper.
Toss the fennel mixture with the lemon vinaigrette and season to taste with salt and pepper. Mound the salad onto the center of 4 serving plates. Arrange the grapefruit segments alongside and serve immediately.
Make-ahead: The fennel can be sliced, submerged in water, and chilled up to 8 hours ahead.