Heat oven to 425 degrees F. Place tomatoes (cut sides up), onion, and garlic on a rimmed baking sheet. Roast for 30 minutes or until tomato skins are charred. Peel off tomato skins.
Place tomatoes in food processor. Cover; process until smooth. Transfer to a large serving bowl. Place onion, garlic, cucumber, sweet pepper, and chile peppers in food processor. Cover; pulse with on/off turns until chopped to desired consistency.
Add processed vegetables, vegetable juice, lemon juice, olive oil, sugar, salt, and black pepper to tomatoes. Stir to combine. Cover; chill at least 4 hours or up to 24 hours.
Spoon gazpacho in bowls. Top with crabmeat. If desired, sprinkle with chives.