Fill a large pot with water and bring to a boil. Core each tomato and cut a small "x" in the skin on the opposite end. Lower 2 or 3 tomatoes into the boiling water and let blanch for 15 to 20 seconds or until the skins start to peel. Immediately transfer the tomatoes to a large bowl of iced water. Blanch the remaining tomatoes in the same manner. Peel each tomato by pulling the skins off with a paring knife. Cut each tomato in half crosswise and squeeze out the seeds. Coarsely chop the seeded tomatoes.
In a blender or food processor puree the garlic clove and the chopped tomatoes. Add the broth, cumin, salt, pepper, and 1 tablespoon lime juice, continuing to puree until smooth. Pour the soup into a metal bowl, set the bowl in a bowl of iced water, and stir the soup occasionally until it is very cold. Taste and adjust seasoning with Tabasco, salt, pepper and lime juice. Divide the avocado and the chives between two chilled bowls and ladle the soup over them.