Slice the chicken breasts horizontally to create a total of 4 thin steaks. Season both sides with salt and pepper.
Place the flour in a shallow bowl and dredge each piece of chicken in it, shaking off any excess.
In a large skillet over high heat, melt most of the butter, reserving about 1 teaspoon for later use.
Add the chicken to the hot skillet and cook for 2 to 3 minutes on the first side until golden brown. Flip and cook for an additional minute on the other side.
Reduce the heat slightly to medium-high.
Push the chicken to the side of the pan to create a bit of space, then add the garlic along with the reserved teaspoon of butter. Once the butter melts, stir the garlic briefly to release its flavor.
Pour in the vinegar, soy sauce, and honey. Stir or shake the pan gently to mix everything together. Allow the sauce to come to a simmer, and cook for about 1 minute or until it slightly thickens.
Turn the chicken pieces in the sauce to coat them evenly. If the sauce becomes too thick, simply add a small splash of water and stir to loosen it.
Remove the skillet from the heat right away. Transfer the chicken to serving plates and spoon the remaining sauce over the top.