Combine corn, pineapple skin, apple skin, cinnamon sticks, cloves and 2 quarts of the water to a boil. Reduce to a simmer and let it cook for 30 minutes. Strain. Reserve 1 piece of pineapple skin and 1 blue corn cob.
Return strained liquid to the pot and add the remaining 2 quarts of water, lime juice and sugar.
Bring to a boil again. Reduce to a simmer and cook for another 30 minutes.
In a large pitcher, place the reserved pineapple and corn cob. Pour Chicha Morada into pitcher and chill in the refrigerator. The flavors will continue to infuse the liquid as it is chilling.