Put the tomatoes, watermelon, cucumber, lime and jalapeno in a food processor or blender and puree until very smooth. Season with salt and chili, to taste. Set aside.
In a bowl, mix together the finely diced cucumber, watermelon, avocado, and lime juice and season with a pinch of salt.
Divide the gazpacho into bowls, top with a heaping spoonful of the diced cucumber-watermelon mixture, and a drizzle of olive oil, if desired.