Pat those chicken breasts dry (moisture = soggy chicken, nobody wants that!). Grab your sharpest knife and thinly slice those bad boys into thin pieces, then pound them flat (underneath some plastic wrap). Season them with salt and pepper.
Dredge & Fry Party: Set up your breading station with a bowl of flour. Dredge each chicken piece, making sure they're coated evenly. Heat up olive oil in a skillet over medium heat. Once it's hot and shimmery, add your floured chicken and cook for a few minutes minutes per side, until golden brown and cooked through. Don't overcrowd the pan, or you'll end up with steamed chicken (yuck!).
The "Almost Gourmet" Sauce: Take that cooked chicken out and give it a rest on a plate. In the same pan (because dishes are overrated), add the garlic and cook it for 30 seconds, until fragrant. Pour in the chicken broth (or wine, if you're feeling fancy) and scrape up all those yummy browned bits from the bottom (flavor central!). Stir in lemon slices and bring the mixture to a boil. Let it simmer until the sauce reduces to about 2/3 cup, 5 to 8 minutes. stir in the lemon juice (use fresh, if you use the bottled stuff use less, because it is more pungent), and capers. Simmer until sauce is reduced and slightly thickened, about 5 minutes more.
Drop butter into the skillet and swirl it into sauce by tilting the skillet until butter is melted and incorporated.
Plating Perfection (Optional): Add your cooked chicken back to the pan and let it simmer in that delicious sauce for a minute or two. Plate it up, garnish with fresh herbs (because #aesthetic), and snap a pic for the 'gram before you devour it!