Place olive oil in a large sauce pot over medium-low heat. Saute onion and garlic in the hot oil until softened, 3 to 4 minutes.
Add chicken broth, chicken breasts, lemon zest, and red pepper flakes to the pot. Increase heat to high, cover, and bring to a boil. Reduce heat to medium and simmer for 5 minutes. Stir in pearl couscous, salt, and pepper. Simmer for 5 minutes more. Remove from heat.
Remove chicken breasts from the pot using tongs. Use a fork and the tongs to shred the chicken. Return to the pot. Stir feta cheese and chives into the soup. Taste and season as needed. Serve warm.