Heat half the olive oil in a sauté pan, season the chicken and brown it all over. Add the garlic and mushrooms then sauté well, tossing around a little to mix.
Put the pan (if oven-proof, or transfer to a roasting tray if not), covered, in the oven and cook for about 20 minutes then remove and leave to rest.
While the chicken is in the oven, bring a large pan of salted water to the boil and cook the pasta for about 3 to 4 minutes, until al dente.
Drain the fettuccine, put back in the pan and then add the remaining olive oil, chilli flakes and lemon zest and juice and stir well.
Add the chicken, garlic and mushrooms, stir well, add the parsley and check the seasoning.