Bring chicken broth to a boil.  Add heavy cream and return to boil.  Slowly whisk in the grits. Reduce heat to a simmer and cook, stirring, until grits are very tender, 20 to 45 minutes depending on how coarse the grits are.

While the grits are cooking, melt butter in a heavy skillet over medium heat. Add the corn and cook, stirring ocasionally, until the corn is soft and beginning to brown in spots. Scrape the contents of the skillet into the grits, taste, and add salt and pepper to taste. Serve warm.