Heat olive oil in a 5-quart / 4.7L pot over medium-high heat. Season chicken chunks with salt and pepper, add to the pot, and sear for 5 to 6 minutes, stirring occasionally, until golden on the outside. Remove chicken to a plate.
Lower heat to medium. Add the onion, carrots, and celery to the same pot. Cook for 5 to 6 minutes, stirring often, until the vegetables soften.
Stir in the garlic, tomato paste, oregano, and thyme. Cook for 1 minute, until fragrant and the tomato paste darkens slightly.
Pour in the diced tomatoes and chicken broth. Return the chicken and any juices to the pot. Bring to a boil, then lower heat and simmer for 12 to 15 minutes, until the chicken reaches 165 F / 74 C and is no longer pink in the center.
Stir in the orzo. Simmer for 8 to 9 minutes, stirring every couple of minutes so it doesn't stick to the bottom, until the orzo is tender but still has a little bite.
Turn off the heat. Stir in the spinach and lemon juice, and let it sit for about 1 minute, just until the spinach wilts.
Taste the broth and adjust salt and pepper, keeping in mind the feta will add more salt later.
Ladle the soup into bowls and top with crumbled feta and chopped dill or parsley. Serve hot.