Heat the butter in a medium saucepan over medium-low heat until melted, then add the garlic and cook, stirring frequently, until fragrant and lightly golden, about 1 minute. Add the chicken broth and increase the heat to medium-high. Bring to a boil, then turn the heat down to low and add the polenta, whisking. Cook, stirring regularly, until thick and creamy, about 10 minutes. Add the Parmesan, heavy cream, chives and pepper and stir to combine. Add salt to taste and serve immediately.