1 large lemon, finely grated to yield 1 tsp. zest and squeezed to yield 3 Tbs. juice
1 lb. asparagus, trimmed and cut into 2-inch pieces
2 Tbs. chopped fresh dill
2 Tbs. unsalted butter, cut into 3 or 4 pieces
Using a meat mallet, pound each chicken breast between 2 sheets of plastic wrap to an even 1/4- to 1/2-inch thickness.
In a shallow bowl, combine the flour, 2 tsp. salt, and 1 tsp. pepper.
Heat 2 Tbs. of the oil in a 12-inch skillet over medium-high heat. Dredge 2 paillards in the flour, shaking off any excess, and place in the skillet. Cook, flipping once, until lightly browned, about 4 minutes total. Transfer the chicken to a plate; set aside. Repeat with the remaining oil and paillards.
Add the garlic to the skillet and cook over medium-high heat, stirring occasionally, for about a minute. Add the chicken broth and lemon zest, scraping up any browned bits from the skillet.
Add the asparagus, chicken, and any accumulated juice and nestle the chicken into the liquid. Bring to a boil, turn the heat down to maintain a simmer, cover, and cook until the chicken is cooked through and the asparagus is tender, 5 to 7 minutes. Transfer the chicken to a platter or plates.
Remove the skillet from the heat and stir in the lemon juice, dill, and butter. Season to taste with salt and pepper. Spoon the asparagus mixture over the chicken and serve.