If the chicken breasts are thick, slice them vertically in half 1" thickness. Combine flour, salt and pepper in medium bowl. Dredge chicken in flour mixture.
Melt 2 tablespoons of butter in large skillet over medium heat. Sauté chicken until cooked through, about 10-12 minutes per side. Set aside and cover to keep warm.
Add remaining tablespoon of butter to pan. Sauté onions in butter until just starting to brown, about 2 minutes, then add mushrooms. Continue cooking until mushrooms soften and reduce in size, about 5 minutes. Add wine and reduce to simmer.
Mix corn starch in chicken broth and add to pan. Season with thyme, salt and pepper, adjusting to taste. Let simmer until gravy thickens. Spoon over chicken.
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