Preheat oven to 350°. Place beaten eggs, sugar, corn syrup, melted butter and vanilla in large mixing bowl and stir until combined well. Fold in pecans. Pour mixture into pie shell, smoothing out top with spoon so pecans are evenly distributed. Carefully place pie in oven and bake until deep nut brown and knife inserted in center of pie comes out clean, 50 to 55 minutes. Remove pie from oven to cool 30 minutes. Cool, slice and serve.