Combine broth, pasta, oil, lemon zest, 1 teaspoon salt, ¼ teaspoon pepper, and ½ cup water in a large straight-sided skillet. Bring to a boil over medium-high and cook, stirring occasionally, 9 minutes.
Season chicken generously with salt and pepper; add to skillet. Continue to cook, stirring, until pasta is al dente and chicken is cooked through, about 3 minutes more.
Remove from heat; stir in lemon juice and dill. Serve immediately, topped with more lemon zest and dill, and a generous drizzle of oil.
