Melt butter in heavy large pot over medium heat. Add onion, garlic, and thyme; sauté until onion is soft, about 8 minutes. Add 4 cups broth, coconut milk, and beans; bring to boil. Reduce heat to medium-low, cover, and simmer until beans are tender, stirring occasionally, 1 1/4 to 1 3/4 hours. Remove thyme sprig.
Set aside scant 1 cup of beans. Working in batches, purée remaining mixture in blender until smooth. Return soup to same pot; add reserved beans and Sherry. (Can be made 1 day ahead. Cover; chill.) Bring to simmer, thinning with broth if desired; keep warm.
Place rum in heavy small skillet. Bring to simmer. Carefully ignite rum. When flames subside, divide soup among 6 bowls, drizzle with rum, sprinkle with chives, and serve.
*Available at many supermarkets and at Indian, Southeast Asian, and Latin markets.
