1. Trim stalks from fennel. Rinse feathery green leaves; chop enough to measure 2 to 3 tablespoons and save a few others for garnish. Discard remaining leaves and stalks. Trim root end, any bruised areas, and coarse fibers from fennel head. Rinse head and cut into paper-thin slices. In a bowl, combine chopped leaves, sliced fennel, and chicken.
2. Cut dates lengthwise into 1/2-inch-wide slices; discard pits. Add dates to bowl.
3. Rinse tangerines and cut in half crosswise. Ream juice from 1/2 the fruit and add to bowl. Cut remaining tangerines (including peel) vertically into paper-thin slices, discarding seeds; add to bowl, along with vinegar and oil. Sprinkle mixture with cayenne, mix gently, and spoon onto plates. Garnish with a few of the reserved green fennel leaves. Add salt to taste.
Note: Nutritional analysis is per serving.