Heat 1 tablespoon olive oil in a large pot over medium to medium-low heat.
Add the thinly sliced chicken, chopped onion, chopped celery, and chopped carrot to the pot; season with salt and pepper and cook until the chicken is no longer pink, about 5 minutes, stirring occasionally.
Stir in the minced garlic and cook for about 30 seconds until fragrant.
Pour in 6 cups chicken broth, then add 1 pound uncooked orzo and 3 tablespoons minced parsley. Stir to combine.
Reduce heat to low and simmer, stirring frequently, until the orzo is al dente and the liquid is mostly absorbed, about 15 minutes.
Taste and adjust seasoning with salt and pepper if needed, then serve warm.