Preheated broiler or grill; pasta pot of boiling water. The following steps occur simultaneously.
In a small saucepan, bring the broth to a boil over high heat. Stir in the sun-dried tomatoes and remove the pan from the heat; let stand for 15 minutes or until the tomatoes soften.
Cook chicken breasts until no longer pink. Transfer to a cutting board and allow to cool. When cool, cut into 1/2-inch cubes.
Add pasta to boiling water, return to boil and cook until tender. Drain the pasta in a colander and transfer to a large bowl for mixing.
Place parsley, vinegar, thyme, garlic, shallots and black pepper in a food processor. Add the sun-dried tomatoes and broth, process until finely chopped.
Combine pasta (in the bowl) with pesto. Add the cut chicken and rough-cut olives; toss to combine. Garnish with tips of fresh thyme sprigs. Serve warm or at room temperature.