Prepare the chicken breasts by slicing them thinly.
Season the flour with salt and pepper on a plate.
Dredge each chicken cutlet in the flour mixture and shake off excess.
In a large skillet, heat olive oil over medium-high heat.
Add the chicken to the skillet in batches, cooking until golden brown.
Remove the chicken and set aside; add butter to the skillet.
Pour in the white wine, scraping up brown bits from the pan.
Add lemon juice and zest, then return the chicken to the skillet.
Finish with fresh parsley and adjust seasoning as desired.