Use a large frying pan for this dish. Add the oil to the pan on a medium heat. When the oil is hot add the chicken pieces. Fry for approximately 5 minutes turning regularly.
Add the garlic, the strips of lemon peel and the lemon juice. Turn the heat down to low and cook for about 10 minutes.
Add the white wine, parsley, salt, pepper and sugar to the pan and cook for a further 10-15 minutes, until the sauce has reduced a little. The sauce should not be too thin but also should not be think. If it does get a little thick add a drop more wine.