Saute the onion in butter in a large saucepan over medium heat, stirring constnatly, until tender. Add tomato, cucumber, chicken broth and basil. Bring to a boil; reduce heaet, and simmer, uncovered, 30 minutes, stirring frequently.
Transfer half of the tomato mixture to a blender, cover and process until smooth. Repeat the procedure with the remaining mixture. (Or use an immersion blender). Stir in the yogurt and salt. Cover and chill. To serve, ladle into individual soup bowls. Garnish with fresh chopped mint.