Pound chicken breast with a meat mallet between 2 sheets of plastic wrap so they are an even thickness--about 1/2-inch/1.25-cm. With smaller or thinly sliced breasts this may not be necessary.
Heat the oil and the butter in a large skillet over medium-high heat. Dredge the chicken in the flour then brown on both sides in the hot skillet. This will depend on the size of the chicken breast but about 4-5 minutes each side would be a good estimate. Don't overcook!
Remove the chicken to a plate and cover to keep warm.
Add the onion/shallot to the hot skillet in which you browned the chicken. Cook for 1 minute, stirring constantly.
Add the remaining sauce ingredients. Stir this well and cook over medium-high heat until the sauce is reduced about 50 percent. It should be thick enough to coat a spoon.