In a large skillet over medium-low heat, heat oil. Cook garlic, stirring, until softened and fragrant, 2 to 3 minutes. Add lemon zest and cook, stirring, until fragrant, about 30 seconds more.
Increase heat to medium. Add orzo, salt, and pepper and cook, stirring, until orzo is slightly toasted, about 1 minute. Pour in 1 cup broth and bring to a simmer, stirring frequently. Once pasta starts to absorb the broth and the liquid reduces by half, add another 1 cup broth. Continue to cook, stirring and repeating with remaining 1 cup broth, until a creamy sauce forms and pasta is al dente, about 10 minutes total; season with salt.
Remove from heat. Stir in cheese, parsley, lemon juice, and chives.
