Heat olive oil in a large pot over medium heat. Add onion, carrots, and celery. Cook until softened, about 5 minutes.
Add garlic and cook for another minute.
Add chicken pieces and cook until they start to brown, about 5 minutes.
Pour in chicken broth, quinoa, bay leaves, and thyme. Bring to a boil, then reduce heat and simmer for 15-20 minutes, or until quinoa is cooked and chicken is tender.
Stir in spinach and cook until wilted, about 2 minutes.
Remove bay leaves. Add lemon juice and zest.
Season with salt and pepper to taste.
Serve hot, garnished with fresh dill if desired.