Preheat oven to 350º. In a large bowl, beat the cream cheese and sugar until light and fluffy. Add the eggs, beat well. Add the sour cream and vanilla, mix well. Place 1 cup of the mixture in a small bowl and stir in the orange extract and the yellow and red food colors.
Pour the remaining cream cheese mixture into the pie crust. Drop the orange cream cheese mixture into it by spoonfuls and swirl with a knife to create a marbled effect. Bake for 30-35 minutes or until firm around the edges. The center will be slightly loose. Allow to cool for 1 hour then cover and chill for at least 8 hours before serving.