Place chicken breasts in a shallow pan and cover with water. Bring to a gentle simmer and cook until just firm, about 12 minutes. Remove and let cool slightly, then shred into bite-sized pieces.
Heat olive oil in a large pot over medium heat. Add chopped onion and sauté until translucent and fragrant, about 5 minutes, until it starts to turn golden around the edges.
Add minced garlic to the pot and cook for another minute, until you smell the aroma and the garlic turns lightly golden.
Pour in the chicken broth and add lemon zest. Bring the mixture to a gentle simmer, allowing the flavors to meld and the broth to brighten, about 10 minutes.
Stir in the shredded chicken and season with salt and pepper. Let it simmer for another 5 minutes so the flavors combine well.
Remove the soup from heat and stir in the freshly squeezed lemon juice. Taste and adjust seasoning if needed.
Chop fresh herbs and sprinkle over the soup just before serving, adding a fresh, grassy note.
Ladle the hot soup into bowls, ensuring each serving has plenty of chicken and bright broth. Serve immediately, garnished with extra herbs and a squeeze of lemon if desired.