Cook fettuccine in salted water until just getting tender and drain well.
Cook broccoli florets in boiling water for 3 minutes and drain.
In a large saucepan, saute chicken pieces in olive oil until done. Remove and set aside.
In same pan melt butter and add jar alfredo sauce, milk, garlic, salt and pepper. Heat for 2 minutes without boiling. Add parmesan cheese and stir to melt. Add chicken pieces, cooked pasta and broccoli florets lightly tossing to coat.