Heat olive oil in a large pot over medium heat.
Add diced onion, garlic, carrots, and celery. Sauté until softened, about 5-7 minutes.
Stir in the chicken and season with salt, pepper, thyme, and oregano; cook for another 2-3 minutes.
Pour in the chicken broth and bring to a boil.
Add the rice, reduce heat to low, and simmer for 15-20 minutes, or until rice and chicken are cooked through.
In the last 5 minutes of cooking, stir in chopped spinach or kale.
Taste and adjust seasoning if necessary before serving.