In a 6-qt. stockpot, heat oil over medium heat. Cook chicken and season with salt and pepper.
Remove chicken from pot and set aside.
Add carrots, onion and garlic. Saute until carrots are tender, 4-5 minutes.
Shred chicken and set aside.
Stir in broth, chicken, and orzo. Bring to a boil. Reduce heat; simmer, uncovered, 5 minutes.
Stir in peas, spinach and dill; return to a boil. Reduce heat; simmer, uncovered, until orzo is tender, 3-4 minutes. Stir in lemon juice. If desired, top each serving with coarsely ground pepper.