Melt 1/4 cup butter in heavy large deep skillet over medium heat. Add the leeks and cook until translucent, stirring frequently, about 4 minutes. Add 4 cups stock and bring to boil. Reduce heat, cover and simmer until leeks are tender, about 25 minutes. Purée mixture in batches in blender.
Melt remaining 1/4 cup butter in heavy large non aluminum saucepan over medium heat. Add flour and stir 2 minutes. Blend in half and half 1 cup at a time; whisk until smooth. Add 1/4 of cheese and blend until smooth and melted. Repeat with remaining cheese in batches.
Strain soup through fine sieve, pressing with back of spoon. Return to saucepan. Mix in leek purée. (Can be prepared 8 hours ahead. Cool, cover and refrigerate.) Rewarm soup over low heat, stirring constantly. Thin with more stock if desired. Season with salt. Ladle soup into bowls. Sprinkle with pepper and chives.