Slice each chicken breast horizontally to yield four thinner fillets. Season both sides of the chicken evenly with salt and pepper.
Place the flour in a shallow bowl and dredge each chicken fillet, shaking off any excess.
In a large skillet over high heat, melt the majority of the butter, reserving approximately 1 teaspoon.
Sear the floured chicken pieces in the hot butter for about 2 to 3 minutes on the first side until golden. Flip and cook the second side for 1 minute.
Lower the heat slightly to medium-high. Push the chicken aside and add the minced garlic to the cleared space, topping it with the reserved butter. Sauté briefly until aromatic and butter has melted.
Pour in the vinegar, soy sauce, and honey. Stir or swirl the pan to meld the ingredients and bring the sauce to a gentle simmer. Let it cook for 1 minute, or until it thickens slightly.
Turn the chicken pieces within the sauce to ensure they are well coated. If the sauce becomes overly thick, incorporate a small amount of water to loosen it.
Remove the pan from the heat. Transfer the chicken to serving plates and spoon over the remaining sauce.