Place the chicken fillets, one at a time between two sheets of plastic wrap

Using either a rolling pin or the flat side of a meat mallet, flatten the fillets to ¼-inch thickness

Season the chicken cutlets with salt and pepper to taste.In a large skillet, heat the olive oil and 2 tablespoons butter over medium-high heat until the butter begins to foam

Add two of the pieces of chicken (aka paillards) and cook on one side until golden brown, about 2-3 minutes

Reduce the heat to medium and flip until the chicken is cooked through, about 2-3 minutes longer

Transfer to a plate

Increase the heat back to medium-high, and repeat with two remaining pieces of chicken, remove the chicken onto the plate.Add the shallot to the skillet, and cook over medium heat, until softened, about 2-3 minutes add the garlic and cook until fragrant, about 1 minute.Add the lemon juice and chicken stock and return the heat to medium-high

Bring to a simmer while deglazing the pan, gently scraping the brown bits from the bottom

Simmer until the sauce reduces by ½ and slightly thickens about 3-4 minutes

Stir in the remaining 4 tablespoons butter and cook just until melted

Adjust seasoning to taste.Add the lemon zest and chives, stir to combine

Place all of the chicken back into the pan along with any juices left on the plate

Heat until warmed through

Serve with a simple green salad alongside