Combine chicken broth and 1 tablespoon butter in heavy medium saucepan and bring to boil. Stir in grits. Reduce heat; cover and simmer 5 minutes, stirring occasionally. Mix cream cheese and half and half into grits. Cover and simmer mixture until almost all liquid has evaporated and grits are tender, stirring frequently, about 7 minutes. Stir in green onions. Remove mixture from heat.
Melt remaining 3 tablespoons butter in heavy large skillet over medium-high heat. Add shrimp and sauté just until shrimp are cooked through, about 3 minutes. Stir in lime juice. Remove skillet from heat. Spoon grits onto center of plate. Top with shrimp and drizzle with lime butter from skillet.
