How to Make It
Bring a large pot of water to a boil. Add the tomatoes and blanch until the skins are loosened, about 30 seconds. Transfer the tomatoes to a large rimmed baking sheet and let cool.
Peel the tomatoes and halve them crosswise. Working over a coarse sieve set over a large bowl, squeeze the tomato halves to release the seeds and juices. Press on the seeds; you should have about 2 cups of tomato juices in the bowl. Coarsely chop enough of the tomatoes to make 4 cups. Cut the remaining tomatoes into 1/2-inch dice.
In a food processor, puree the coarsely chopped tomatoes with the reserved tomato juice and the 2 cups each of chopped watermelon and cucumber. Transfer the soup to a large bowl. Stir in the diced tomato, watermelon and cucumber, the vinegar and 1 tablespoon of the olive oil and season with salt and pepper. Refrigerate until chilled, at least 1 hour.
In a small bowl, mix the scallions, jalapeños, cilantro and lime juice; season with salt and pepper. Ladle the soup into bowls, drizzle with the remaining 2 tablespoons of olive oil and sprinkle the chives on top. Pass the scallion relish at the table.