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Preheat oven to 375 degrees.
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In medium bowl, toss mushrooms with 1/2 Tbsp of oil. Spread on rimmed baking sheet and bake for 10-15 minutes.
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Heat remaining 1 Tbsp oil over medium heat. Season chicken with salt and pepper. Brown chicken on both sides. Remove chicken from pan and finish cooking in the oven for 15 minutes.
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Melt butter in the pan. Stir in flour and cook for one minute. Slowly stir in chicken broth, scraping the bottom of the pan, letting each addition incorporate before adding more.
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Slowly add wine and sugar. Bring to a boil. Reduce heat and simmer for 15 minutes or until slightly thickened.
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Serve chicken with mushrooms and red wine sauce.