1. In a 5- to 6-quart pan over high heat, frequently stir shallots, thyme, and 1/2 cup broth until vegetables are lightly browned, 5 to 7 minutes. Add 6 1/2 cups broth and chestnuts. Cover, bring to a boil, then reduce heat and simmer until chestnuts mash easily, about 30 minutes.
2. Whirl mixture, a portion at a time, in a blender until it is very smooth. Or, with a slotted spoon, skim chestnuts and vegetables from broth and purée in a food processor, then mix with broth in pan.
3. Measure soup. If you have less than 6 cups, add broth to make this amount and return to pan and stir until hot. If you have more, boil and stir until soup is reduced.
4. Ladle hot soup into bowls. Add a spoonful of sour cream to each and sprinkle with chives. Season with salt to taste.