Bring a medium saucepan of well-salted water to a boil over high heat. Meanwhile, heat the oil in a large soup pot over medium heat. Add the celery, onion, saffron, and thyme. Cook, stirring occasionally, until the vegetables start to soften, 5 to 6 minutes. Add the broth and bring to a boil over medium-high heat. Reduce the heat to a simmer, add the chicken and cook until the vegetables are tender, about 15 minutes. While the soup simmers, cook the orzo in the boiling salted water until tender, 8 to 10 minutes. Drain.

Add the drained orzo, corn, and parsley to the soup and cook just until the corn is heated through, about 2 minutes. Stir in the lemon juice and season to taste with salt, pepper, and more lemon juice, if needed.

You might wonder why the orzo is cooked separately. There are two reasons. If you boiled the orzo directly in the soup, the starch from the pasta would cloud the soup broth, and the orzo would also suck up too much of the soup broth as it cooked. Boiling the pasta separately solves both of these problems.