Bring large saucepan of water to boil. Drop in 3 tomatoes; cook 30 seconds. Using slotted spoon, transfer tomatoes to plate. Repeat. When cool, peel tomatoes starting at X. Cut tomatoes in half horizontally; squeeze out seeds and juice. Place tomatoes in processor. Using on/off turns, chop to coarse puree. Transfer puree to strainer; let drain 30 minutes, stirring often.
Combine tomato puree, chicken broth, onion, 1/3 cup lime juice, garlic, parsley, chives, and cilantro in large bowl. Season gazpacho with salt and pepper. Chill 2 hours or up to 1 day.
Blend avocados, chiles, 2 tablespoons water, and 1/3 cup lime juice in processor until smooth. Season with salt; add more water to thin if desired.
Ladle gazpacho into bowls. Top with avocado puree, then drizzle of oil.
