Wash shrimp and add to pot with water. Cut orange in half, squeeze it out into the water and add the rinds as well. Squeeze in lemon juice.
Bring to a boil and then lower to a simmer. Add corn and butter. Simmer until corn is tender.
Turn off heat. Strain out most of the water. Remove orange but don't discard. Remove half of the corn and shrimp into separate bowl. Roughly mash the other half in the pot with the remainder of the water.
Return shrimp and corn to pot. Add half and half. Bring to almost a simmer and add cornstarch, stirring away the lumps. Now taste and add salt to your liking. After about 3-4 minutes, turn off heat, cover and let stand for 5 minutes to thicken.
When serving, squeeze what's left of the oranges on top of chowder, and garnish with fresh basil!