Arrange bell peppers, skin side down, and corn in a single layer on a grill rack; grill 5 minutes, turning corn occasionally. Add tomatoes; grill an additional 5 minutes or until vegetables are slightly charred. Remove from heat; cool 10 minutes. Coarsely chop tomatoes and bell peppers; place in a medium bowl. Cut kernels from ears of corn; add to tomato mixture.
Heat oil in a large Dutch oven over medium heat. Add onion; cook 7 minutes or until tender, stirring occasionally. Stir in tomato mixture; cook 3 minutes, stirring occasionally. Increase heat to high, and stir in broth. Bring to a boil. Reduce heat, and simmer 30 minutes or until vegetables are tender. Cool 20 minutes.
Place one-third of tomato mixture in a blender; process until smooth. Place pureed mixture in a large bowl. Repeat procedure twice with remaining tomato mixture. Wipe pan clean with paper towels. Press tomato mixture through a sieve into pan; discard solids. Place pan over medium heat; cook until thoroughly heated. Stir in salt and black pepper. Ladle about 1 1/2 cups soup into each of 6 bowls; top each serving with 2 teaspoons cheese and 1 teaspoon chives.