In a small bowl, combine the flour, salt and pepper.
Dredge the chicken breasts in this mixture, one at a time, and arrange them
on a plate.
In a large skillet, heat the olive oil over medium-high heat.
Add the chicken breasts and cook quickly until lightly browned on both sides,
turning once - 1 to 2 minutes per side. (You may have to do this in two batches.)
The chicken should be browned but not cooked through. Remove to a plate.
Add the butter to the skillet, then add the mushrooms. Cook, stirring frequently,
until the mushrooms have released their liquid and liquid has evaporated.
Pour in the champagne; stir around to dissolve any crusty bits from bottom
of the pan, then stir in the whipping cream. Bring to a boil, then lower the
heat and let the sauce simmer for about 5 minutes.
Return the chicken breasts to the skillet, nestling them into the mushroom
sauce, lower the heat to medium and cook, uncovered, until the chicken is cooked
through and the sauce is thickened - 6 to 8 minutes.
Serve immediately with crusty bread or steamed rice to soak up the velvety