Put the honey and mustard on a plate and mix well. Set it aside.
Put the chicken, smooth side up, on the cutting board, season with salt and pepper and generously cover with plastic wrap.
Using the back of the skillet or a rolling pin, pound the chicken until it is the same thickness all over. (This will help it cook quickly and evenly.)
Put the skillet on the stove and turn the heat to high. When the skillet is hot, add the oil. When the oil is hot, carefully add the chicken and cook until golden on the outside and no longer pink on the inside, about 5 minutes per side.
Use tongs or a fork to add the chicken breasts to the honey-mustard mixture, and swirl around until they are coated on both sides.
Serve right away or cover and refrigerate up to 3 days.