Pearled barley is convenient and relatively quick-cooking; if you want to make this a whole-grain salad, you'll need to choose hulled barley, which takes about an hour to cook.
Cook barley according to package directions. Rinse with cold water.
Combine oil and next 4 ingredients in a large bowl. Add barley, grapes, chicken, and onions; toss well to combine. Add cheese; toss gently to combine. Sprinkle with walnuts and thyme.