Rinse the chicken breasts and dry using kitchen towel paper. Cover them with flour, shake off the excess and season the fillets with salt and pepper. In a large pan heat the oil on a medium setting.
Carefully place the chicken breasts in the pan and cook. Turn the chicken breasts once until both sides are golden brown and the chicken has been cooked through, this will take about 10 minutes. Transfer chicken to a plate and cover with foil to keep warm.
Drain off the excess fat from the pan and add the white wine. The mixture then should be boiled down until it has been reduced by a third. Gently whisk the butter into the mixture. Add salt and pepper and cover over the chicken breasts to serve.
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