Heat olive oil in a large pot over medium heat. Add onion, garlic, and celery; sauté until translucent and fragrant, 5–7 minutes.
Add carrots, diced tomatoes (with juices), and green chilies. Stir in broth, thyme, and bay leaf. Bring to a gentle simmer, cover, and cook 25–30 minutes until carrots are tender.
Stir in cooked barley or rice and shredded chicken (if using). Simmer 5–10 minutes more to heat through. Season with salt and pepper to taste. Remove bay leaf.
Serve hot topped with crispy tortilla strips, chopped cilantro, and a squeeze of fresh lime.
Air Fryer Tortilla Strips: Slice tortillas into 1/4-inch strips. Toss with oil (or spray) and salt; season if desired. Air fry at 375°F (190°C) in a single layer for 5–8 minutes, shaking halfway, until crisp. Cool on paper towel.