Add leek, garlic and thyme to the pan; reduce heat to medium. Cover and cook, stirring occasionally, until the leek is softened, about 4 minutes. Return the chicken to the pan; stir in penne, broth and salt. Bring the mixture to a simmer over medium-high heat. Reduce heat to maintain a simmer; cook, stirring occasionally to prevent sticking, until the pasta is tender and the chicken is cooked through, 9 to 10 minutes, adding asparagus to the mixture during the final 5 minutes of cook time.