Cut peel and pith from each grapefruit. Holding over a bowl, carve out flesh between the membranes, letting segments drop into the bowl. Squeeze membranes over bowl. Strain juice into a measuring cup. Set aside 12 segments; return 1/4 cup juice to the bowl (reserve remaining juice and segments for another use).
Add shallot, vinegar, peppercorns, and salt to bowl with juice; toss. Whisk in oil. Set dressing aside.
Cut each endive in half lengthwise; cut out cores. Cut endive halves lengthwise into thin matchsticks. Toss with celery in a medium bowl. Pour in about three-quarters of the dressing; toss.
Put a small amount of endive and celery onto each of 4 plates, and place a chevre round in center. Arrange 3 grapefruit segments around chevre. Top each salad with remaining endive and celery. Drizzle with remaining dressing, and sprinkle with celery leaves.