Heat oven to 400° F. Toss the chicken, grapes, sliced celery, thyme, red pepper, 2 tablespoons of the olive oil, 1 teaspoon salt, and ½ teaspoon black pepper on a rimmed baking sheet. Roast, tossing once, until the chicken is golden and cooked through, 18 to 20 minutes. Remove from oven and let cool slightly. Discard the thyme sprigs and shred the chicken into bite-size pieces using 2 forks.
Meanwhile, whisk together the yogurt, mustard, vinegar, the remaining tablespoon of olive oil, and ¼ teaspoon each salt and black pepper in a large bowl. Add the chicken, grapes, celery, escarole, and walnuts and toss to combine. Serve with a baguette.