In a 4-quart saucepan cook fettuccine according to package directions, omitting any salt and adding green beans the last 5 to 6 minutes of cooking or the asparagus the last 2 minutes of cooking. Drain and return to pan.
In a large nonstick skillet cook onion, covered, in hot oil over medium heat for 7 to 8 minutes or until starting to brown, stirring occasionally. Add chicken and garlic. Cook, uncovered, for 4 to 6 minutes more or until chicken is no longer pink and onion is very tender, stirring frequently. Reduce heat to low. Add Alfredo sauce, chicken broth, and thyme. Cook and stir until heated through.
Add chicken mixture to cooked fettuccine; toss to coat. Divide fettuccine mixture among six serving plates. Sprinkle with pepper.