Bring a large pot of salted water to a boil over high heat. Add the pasta shells and cook until tender but still firm to the bite, stirring occasionally, 12 to 13 minutes. Drain and cool.
For the dressing: Combine the vinegar, lemon juice, salt, pepper and garlic in a small bowl. Gradually add the oil, whisking until the dressing is thick.
For the salad: In a large bowl, combine the arugula, feta, tomatoes, salt, pepper, olives, chicken, avocado and fennel.
Add the dressing to the salad and toss to coat.
Line each shell with a leaf of radicchio, trimming each leaf if too large for the pasta. Fill shells with salad, pressing slightly so salad will adhere. Arrange shells on a platter and serve.
Recipe courtesy of Giada De Laurentiis