Preheat the oven to 375℉. Spray a 9x13-inch baking dish with nonstick spray.
Bring a large pot of salted water to boil. Cook the pasta for 6 minutes. Drain, and set aside.
In a large skillet over medium-heat, melt the butter and add the olive oil. Add the garlic and cook for 2 minutes. Reduce the heat to low, and add the cream cheese; stir until melted. Stir in the wine, lemon juice. Stir the flour into the sour cream, and then stir that mixture into the pan. Add the chicken broth, red pepper and a sprinkle of salt and pepper. Bring to a simmer until slightly thickened. Then remove from heat.
Stir in ½ cup Parmesan cheese, lemon zest and thyme. Then stir in the partially cooked pasta and cooked chicken. Pour the mixture into the prepared dish. Sprinkle with the remaining Parmesan cheese.
Bake, covered, for 25 minutes. Uncover and continue to bake until lightly browned for 5 to 10 more minutes.