Cut each breast in half lengthwise into cutlets. Measure the flour, salt and pepper into a plastic bag. Add the chicken breasts and shake until completely coated with the flour.
In a large skillet heat the olive oil over medium-high heat, then add the chicken breasts. Fry the breasts on each side about 4 minutes, until golden brown and no longer pink inside. Remove from the pan onto a plate.
Over medium heat, add the garlic to the remaining olive oil in the skillet and cook about 1 minute until the garlic is just starting to turn golden. Add the milk, cream and parmesan cheese to the skillet and bring to a boil. Turn down the heat and simmer the cream mixture for about 5 minutes until it starts to thicken.
Add the capers and lemon juice to the skillet. Start with 2 TBSP of lemon juice and add additional tablespoons one at a time if you like the sauce more tart. Stir to combine. Continue to simmer until the desired thickness, about 3 minutes.
Add the chicken back to the skillet to warm thru. Sprinkle the basil over the top and serve.