Bring a large pot of salted water to a boil over high heat. Add pasta and cook according to package label's directions. While pasta is cooking, place goat cheese, cream, garlic, lemon zest and lemon juice in a small bowl and mash with a fork to combine.
Reserve 1/2 cup cooking liquid and drain pasta. Return pasta to pot and stir in peas, goat cheese mixture and chicken. Stir in cooking liquid. Season with salt and pepper and serve immediately.