Preheat the oven to 350 degrees. In a large bowl, with an electric beater on medium speed, beat the cream cheese and sugar until light and fluffy. Add the eggs and beat well. Add the sourcream and vanilla; mix well.
Place 1 cup of the cream cheese mixture in a small bowl and stir in the orange extract and the yellow and red food color. Pour the remaining cream cheese mixture into the pie crust.
Drop the orange cream cheese mixture by spoonfuls onto the cream cheese mixture in the crust; swirl with a knife to create a marbled effect.
Bake for 30 to 35 minutes, 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.