In a large saucepan, melt the butter over medium heat. Add the leeks, carrots and thyme; season with salt and pepper. Cook, stirring occasionally, until softened, about 10 minutes. Add the chicken broth and peas, cover and bring to a boil. Lower the heat, add 3 1/2 cups water, cover and simmer, stirring occasionally, until the peas begin to break down, 1 hour and 10 minutes.
Stir the vinegar into the soup; season with salt. Ladle into bowls and top each portion with sour cream and chives.
One Quick Trick for Cutting Chives