Cook the pasta according to the package directions; drain and return it to the pot.
Meanwhile, melt the butter in a medium skillet over medium heat. Add the leek, ¾ teaspoon salt, and ¼ teaspoon pepper and cook, stirring occasionally, until tender, 4 to 6 minutes.
Add the cream and 1 tablespoon of the lemon zest and simmer until slightly thickened, 8 to 12 minutes.
Add the chicken and cook until warmed through, 1 to 2 minutes more.
Add the chicken mixture and the remaining tablespoon of lemon zest to the pasta and toss to coat.