One by one, place the chicken breasts between 2 pieces of plastic wrap, or inside of a resealable plastic bag, and pound with a meat mallet or rolling pin or heavy-bottomed pan until about 1/2-inch thick. In a glass baking dish, combine the zest and all but 1 tablespoon of the lemon juice with 1/4 cup of the olive oil, the shallot, garlic, and a little more than 2 tablespoons of each of the chopped fresh herbs. (Reserve the remaining chopped herbs.) Add the pounded chicken breasts to the herb mixture and turn to coat. Season generously with salt and pepper, cover the dish with plastic wrap, and put in the refrigerator to marinate, at least 20 minutes and up to 1 hour.
Heat the remaining 2 tablespoons olive oil in a large saute pan over high heat. Add the chicken breasts to the pan and cook, turning once, until cooked through and golden brown on both sides, about 4 to 5 minutes per side. Cook the breasts 2 at a time if the pan is too small. Transfer to a serving platter and keep warm.
Add the remaining 1 tablespoon of lemon juice and the white wine to the pan, scraping to loosen any brown bits, and reduce until almost dry. Add the chicken broth and reduce by half, then off the heat add the reserved herbs and cold butter, swirling to melt the butter and thicken the sauce. Pour over the chicken paillards and serve immediately.