Heat oil over medium heat in a large, deep skillet with a lid. Sauté the onion, carrot, and garlic with the curry powder and thyme until onion is soft. Add the orzo and sauté until the pasta is lightly browned.
Stir in the chicken broth, chickpeas, and chili sauce; bring to a boil. Cover with a tight-fitting lid and reduce the heat to low. Simmer the stew 12 minutes, stirring occasionally, or until the orzo is fully cooked. (The stew should be a little brothy, not dry.)