Melt the butter in a medium skillet over medium-low heat. Add the leeks and garlic; simmer, stirring occasionally for about 5 minutes.
Add the wine, and simmer until leeks are very tender, about 4 minutes. Add cream and chives; return to a simmer.
Reserve half; transfer the remaining mixture to a blender. Add chicken broth, and puree until the leek sauce is smooth. Return to the pan with the reserved mixture and stir to combine.