In a large stockpot, combine water and parmesan rinds, and bring to a boil. Reduce heat to low, and simmer for 2 hours. Strain broth, and set aside, discarding the parmesan rinds.
In a stockpot over medium-low heat, melt butter. Once melted, add garlic, and cook for 3 minutes, stirring often to ensure garlic does not brown. Add chard, and cook 2 additional minutes.
Add parmesan and chicken broths to the pot, and bring to a boil. Reduce heat to low, and simmer for 15 minutes. Turn off heat, and let soup cool for 5 minutes.
In a blender, puree the soup, working in batches if necessary, until a smooth consistency is achieved and all bits of green have been pulverized. Return soup to pot, and warm over low heat. Add salt and pepper to taste, and serve topped with parmesan shavings.