This recipe -- a riff on the classic Greek dish avgolemono -- is also a great way to use up leftover cooked chicken. First, cut or shred the chicken; then, in step 2, stir it into the pot for the last minute of cooking, just to heat through.
Combine broth, pasta, oil, lemon zest, 1 teaspoon salt, 1/4 teaspoon pepper, and 1/2 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.