Cook the sugar pumpkin and then strain or blend in blender to smooth out the texture. Put the strained pumpkin, approximately 4 cups, into a medium pan and add 1/2 C brown sugar, salt and pepper to taste. It should be a sweet and savory flavor (be sure to taste it to be sure). Cook the mixture on a medium heat until the mixture darkens slightly. Remove from the heat.
In a baking dish place the 4 chicken breasts on the bottom and pour the pumpkin mixture over the top. Cover the dish. Bake at 355 degrees for about 2 to 2.5 hours. Remove the chicken breasts from the baking dish and slice into 1/2 inch slices. Pour the pumpkin mixture onto a serving platter and add the chicken back onto the top of the pumpkin. Garnish if desired and serve hot.