Melt butter in a Dutch oven over medium-high heat. Remove green tops from green onions. Chop green onion tops; set aside. Thinly slice white portion of each onion. Add sliced onions to pan; sauté 2 minutes. Add flour; cook 1 minute, stirring constantly with a whisk. Stir in chicken, salt, pepper, 1 package of corn, and broth; bring to a boil. Reduce heat, and simmer 5 minutes.
While mixture simmers, combine the remaining corn and milk in a blender; process until smooth. Add milk mixture to pan; simmer 2 minutes or until thoroughly heated. Ladle 2 cups chowder into each of 4 soup bowls; sprinkle evenly with green onion tops. Top each serving with 2 tablespoons cheese.