Heat 2 teaspoons olive oil in a large saucepan set over medium-high heat. Add the chicken, salt and pepper, and sauté until just cooked through. Transfer the chicken to a bowl.
Turn the heat to medium and heat the remaining 1 teaspoon of oil in the saucepan. Add the onions and carrots, and cook until the vegetables are starting to soften, about 5 minutes. Add the garlic, oregano and red pepper flakes, and cook for 1 minute.
Stir in the crushed tomatoes and chicken broth. Bring to a boil, then reduce heat and simmer for 20 minutes, stirring occasionally.
Add the orzo and cook until tender, 8 to 10 minutes.
Stir in the chickpeas and heat for about 2 minutes.